Answer:
4 consecutive goals
Step-by-step explanation:
If 3 of last 10 field goals = 30%
Which is equivalent to
(Number of goals scored / total games played) * 100%
(3 / 10) * 100% = 30%
Number of consecutive goals one has to score to raise field goal to 50% will be:
Let y = number of consecutive goals
[(3+y) / (10+y)] * 100% = 50%
[(3+y) / (10+y)] * 100/100 = 50/100
[(3+y) / (10+y)] * 1 = 0.5
(3+y) / (10+y) = 0.5
3+y = 0.5(10 + y)
3+y = 5 + 0.5y
y - 0.5y = 5 - 3
0.5y = 2
y = 2 / 0.5
y = 4
Therefore, number of consecutive goals needed to raise field goal to 50% = 4
What is the measure of B, in degrees?
Answer:
B = 32
Step-by-step explanation:
Since this is an isosceles triangle, C is also equal to 74 degrees
the angles of a triangle add to 180
A + B+ C = 180
74+ B + 74 = 180
148 + B = 180
B = 180-148
B =32
PLEASE ANSWER ASAP!!!
Equation in the picture
Solve for r in the equation in the picture. You must use the LCD (Least Common Denominator) to simplify. You can also use cross products to solve.
Must show work
A. r = 19
B. r = 21
C. r = 25
D. r = 30
any unrelated answer will be reported
Answer:
r = 19
Step-by-step explanation:
( r-5) /2 = ( r+2) /3
The least common denominator is 6
3/3 *( r-5) /2 = ( r+2) /3 * 2/2
3( r-5) /6 = 2( r+2) /6
Since the denominators are the same, the numerators are the same
3( r-5) = 2(r+2)
Distribute
3r -15 = 2r+4
Subtract 2r from each side
3r-2r -15 = 2r+4-2r
r-15 =4
Add 15 to each side
r-15+15 = 4+15
r = 19
Sugar, flour, and oats are stored in three drawers. The first drawer is labeled "oats", the second is labeled, "flour", the third is labeled "oats or flour". The label of each drawer does not correspond to what is stored inside of it. In which drawers is what stored?
Answer:
first = flour, second = oats, third = sugar
Step-by-step explanation:
Since the labels are "wrong", we know that the third drawer doesn't have oats or flour, therefore it has sugar. Since the first doesn't have oats, it must have flour and that makes the second drawer oats.
Answer:
first drawer has flour, second has oats, third is sugar
Step-by-step explanation:
on the first drawer, it is labelled oats, so it cannot be oats. on the second it cannot be flour, and on the third it cannot be oats or flour, which means it HAS to be sugar leaving oats and flour to be in either the first, or second.
i know it may sound a little confusing but please let me know if you dont understand
Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance using the given sample statistics.
Claim: p>0.12; α=0.05; Sample statistics: Modifying above p with caret equals 0.08, n is equal to 250
Answer:
There is no sufficient evidence to support the claim
Step-by-step explanation:
From the question we are told that
The level of significance is [tex]\alpha = 0.05[/tex]
The sample proportion is [tex]\r p = 0.08[/tex]
The sample size is [tex]n = 250[/tex]
Generally for normal sampling distribution can be used
[tex]n * p > 5[/tex]
So
[tex]n* p = 250 * 0.12 = 30[/tex]
Since
[tex]n * p > 5[/tex] then normal sampling distribution can be used
The null hypothesis is [tex]H_o : p = 0.12[/tex]
The alternative hypothesis is [tex]H_a : p > 0.12[/tex]
The test statistic is evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p)}{n} } }[/tex]
substituting values
[tex]t = \frac{0.08 - 0.12 }{ \sqrt{ \frac{0.12 (1- 0.12)}{250 } } }[/tex]
[tex]t = -1.946[/tex]
The p-value is obtained from the z table and the value is
[tex]p-value = P(t > -1.9462) =0.97512[/tex]
Since the [tex]p-value > \alpha[/tex]
Then we fail to reject the null hypothesis
Hence it means there is no sufficient evidence to support the claim
Working together, it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 50 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? don't round
Answer:
12.5 minutes
Step-by-step explanation:
When working together,It takes two computers 10 minutes to send out an email
It takes the slower computer 50 minutes to send out an email
Let x represent the time taken by the faster computer to do the job in its own
Therefore, the time required by the faster computer can be calculated as follows
1/x + 1/50= 1/10
Collect the like terms
1/x= 1/10-1/50
1/x= 4/50
Cross multiply both sides
4 × x = 50×1
4x=50
Divide both sides by the coefficient of x which is 4
4x/4=50/4
x= 12.5
Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes
The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,θ) . Select the correct equation in polar coordinates below.
x2+y2−4x=0
a. r=4 sinθ
b. r=4 cosθ
c. r cos2θ=4 sinθ
d. r sin2θ=4 cosθ
Answer:
B. r = 4cosθStep-by-step explanation:
Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).
x = rcosθ and y = rsinθ.
Substituting the value of x and y in their polar form into the given expression we have;
x²+y²−4x=0
( rcosθ)²+( rsinθ)²-4( rcosθ) = 0
Expand the expressions in parenthesis
r²cos²θ+r²sin²θ-4rcosθ = 0
r²(cos²θ+sin²θ)-4rcosθ = 0
From trigonometry identity, cos²θ+sin²θ =1
The resulting equation becomes;
r²(1)-4rcosθ = 0
r²-4rcosθ = 0
Add 4rcosθ to both sides of the equation
r²-4rcosθ+4rcosθ = 0+4rcosθ
r² = 4rcosθ
Dividing both sides by r
r²/r = 4rcosθ/r
r = 4cosθ
Hence the correct equation in polar coordinates is r = 4cosθ
Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020. If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?
Answer:
The product decreases 2022.
Step-by-step explanation:
(x + 1)(y - 1) = xy + 2020
xy - x + y - 1 = xy + 2020
-x + y = 2021
(x - 1)(y + 1) = xy + x - y - 1
+ 2021 = -x + y
----------------------------------
(x - 1)(y + 1) + 2021 = xy - 1
(x - 1)(y + 1) = xy - 2022
The product decreases 2022.
Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}
Answer:
The answer is 55, -275, 1375, -6875......
Step-by-step explanation:
On dividing polynomial p(x) by a linear binomial, X - a, we get a quotien
statements must be proven true for the remainder theorem to be true
Answer:
Step-by-step explanation:
Hello, we can write
(1) p(x)=(x-a)q(x)+r
[tex]\boxed{\sf v}[/tex] True
It means that p(a)=0 * q(a) + r = r
so the first one is true.
[tex]\boxed{}[/tex] False
The second one is not to be proven true from the remainder theorem.
[tex]\boxed{\sf v}[/tex] True
For x different from a we can divide the equation (1) by (x-a).
[tex]\boxed{}[/tex] False
We cannot say anything on q(a).
[tex]\boxed{\sf v}[/tex] True
If the rest is 0 then it means that p(a) = 0
[tex]\boxed{\sf v}[/tex] True
If p(a) = 0 it means that the rest r = 0 and then p(x)=q(x)(x-a)
Thank you
Write the expression (x4)8 in simplest form.
Answer:
the 4 and 8 are exponents
Step-by-step explanation:
Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?
Answer:
q = 0.105uC
Step-by-step explanation:
We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.
Considering the horizontal and vertical components.
First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:
E=kq/r²
Where r = 20cm
= 20/100
= 0.2m
K = 9.0×10^9
9.0×10^9 × q /0.2²
9.0×10^9/0.04
2.25×10^11 q
These are vector fields of course
Sum the horizontal components
Ecos0 + Ecos300 = E+0.5E
= 1.5E
Sum the vertical components
Esin0 + Esin300 = -E√3/2
Resultant = √3E at -30° or 330°
So the force on q at the lower right corner is q√3×E
The balls have two forces, horizontal = √3×E×q
and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg
mg×tanθ = q√3E.
..1
Then θ will be...
Since the hypotenuse = 80cm
80cm/100
= 0.8m
The distance from the centroid to the lower right vertex is 0.1/cos30 =
0.1/0.866
= 0.1155m
Hence,
0.8×sinθ = 0.1155
Sinθ = 0.1155/0.8
Sin θ = 0.144375
θ = arch sin 0.144375
θ = 8.3°
From equation 1
mg×tanθ = q√3E
g = 9.8m/s^2
m = 3.0g = 0.003kg
0.003×9.8×tan(8.3)
0.00428 = q√3E
0.00428 = q×1.7320×E
Where E=kq/r²
Where r = 0.2m
0.0428 = kq^2/r² × 1.7320
K = 9.0×10^9
0.0428/1.7320 = 9.0×10^9 × q² / 0.2²
0.02471×0.04 = 9.0×10^9 × q²
0.0009884 = 9.0×10^9 × q²
0.0009884/9.0×10^9 = q²
q² = 109822.223
q = √109822.223
q = 0.105uC
Twice the difference of a number and 9 is 3. Use the variable b for the unknown number.
Answer:
b = 10.5
Step-by-step explanation:
2(b-9) = 3
then:
2*b + 2*-9 = 3
2b - 18 = 3
2b = 3 + 18
2b = 21
b = 21/2
b = 10.5
check:
2(10.5 - 9) = 3
2*1.5 = 3
Use Lagrange multipliers to find three numbers whose sum is 30 and the product P = x3y4z is a maximum. Choose the answer for the smallest of the three values. Question 20 options: a) 21/4 b) 5 c) 15/4 d) 3
We want to maximize [tex]x^3y^4z[/tex] subject to the constraint [tex]x+y+z=30[/tex].
The Lagrangian is
[tex]L(x,y,z,\lambda)=x^3y^4z-\lambda(x+y+z-30)[/tex]
with critical points where the derivatives vanish:
[tex]L_x=3x^2y^4z-\lambda=0[/tex]
[tex]L_y=4x^3y^3z-\lambda=0[/tex]
[tex]L_z=x^3y^4-\lambda=0[/tex]
[tex]L_\lambda=x+y+z-30=0[/tex]
[tex]\implies\lambda=3x^2y^4z=4x^3y^3z=x^3y^4[/tex]
We have
[tex]3x^2y^4z-4x^3y^3z=x^2y^3z(3y-4x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\z=0,\text{ or}\\3y=4x\end{cases}[/tex]
[tex]3x^2y^4z-x^3y^4=x^2y^4(3z-x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\3z=x\end{cases}[/tex]
[tex]4x^3y^3z-x^3y^4=x^3y^3(4z-y)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}4z=y\end{cases}[/tex]
Let's work with [tex]x=3z[/tex] and [tex]y=4z[/tex], for which we have
[tex]x+y+z=8z=30\implies z=\dfrac{15}4\implies\begin{cases}x=\frac{45}4\\y=15\end{cases}[/tex]
The smallest of these is C. 15/4.
Give this problem a try and try to solve this
Answer:
No solution
Step-by-step explanation:
Given equation is,
[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}-\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}=0[/tex]
[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}=\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}[/tex]
[tex]\frac{(x+1)}{\sqrt{x}(1-x)}+\frac{(\sqrt{x}-1)}{\sqrt{x}(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]
[tex]\frac{(\sqrt{x}+1)(x+1)+(\sqrt{x}-1)(1-x)}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]
[tex]\frac{x\sqrt{x}+x+\sqrt{x}+1+\sqrt{x}-1-x\sqrt{x}+x}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]
[tex]\frac{2x+2\sqrt{x}}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]
[tex]\frac{2(\sqrt{x}+1)}{(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]
[tex]\frac{2}{1-x}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex] if x ≠ ±1
[tex](\frac{2}{1-x})^2=\frac{4+x}{1-x}[/tex] [Squaring on both the sides of the equation]
[tex]\frac{4}{(1-x)}=(4+x)[/tex]
4 = (1 - x)(4 + x)
4 = 4 - 4x + x - x²
0 = -3x - x²
x² + 3x = 0
x(x + 3) = 0
x = 0, -3
But both the solutions x = 0 and x = -3 are extraneous solutions, given equation has no solution.
Answer:
Could you please help me Genius??????
On a class trip with 40 students, 14 are male. What percentage of the class is female?
66%
60%
65%
58%
Answer:
65%
Step-by-step explanation:
If 14 are male, then 26 are female.
To find the percent female, divide the number of females by the total.
26/40 = 0.65
So, the percentage of the class that is female is 65%
Answer:
C. 65%
Step-by-step explanation:
We know that of the 40 total students, 14 are male, which means the remaining students are female.
To find how many are female, we subtract 14 from 40:
40 - 14 = 26 females
Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:
(26 / 40) * 100 = 65
The answer is thus C, 65%.
~ an aesthetics lover
Today only, a suit is being sold at a 26% discount. The sale price is $259.
What was the price yesterday?
Answer:
$350
Step-by-step explanation:
1. Set up the equation. The sale price of $259 is 74% of the original price.
[tex]\frac{74}{100}[/tex] = [tex]\frac{259}{x}[/tex]
2. Cross multiply
74x = 25900
3. Solve
x = 350
7 1/4 x−x=9 3/8 HELLLLPPPPP PLLSSSS
-1.5
Step-by-step explanation:
So, you do 7.25 - 1 (because it is) and you get 6.25. Make it a fraction inton 25/4 and divide bu 75/8 (9 3/8 simplified) and you get -1.5 voila.
Answer:
x = 3/2
Step-by-step explanation:
7 1/4 = 7 + 1/4 = 28/4 + 1/4 = 29/4
9 3/8 = 9 + 3/8 = 72/8 + 3/8 = 75/8
then:
7 1/4 x = 29x/4
29x/4 - x = 75/8
29x/4 - 4x/4 = 75/8
25x/4 = 75/8
x = (75/8)/(25/4)
x = (75*4)/(8*25)
x = 300/200
x = 3/2
Checking:
(29/4)(3/2) = (29*3)(4*2) = 87/8
87/8 - 3/2 = 75/8
3/2 = 12/8
then:
87/( - 12/8 = 75/8
Please help me with this question
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...
-x^2 +10x ≥ 0
x(10 -x) ≥ 0
The two factors in this product will both be positive only for values ...
0 ≤ x ≤ 10 . . . . the domain of f(x)
Your friend Iggy tells you that the product of 80 and 70 will have four zeroes. Explain to Iggy why his estimation is incorrect, and how to fix it.
4 zeroes basically means [tex]10^4[/tex]
$80=2^3\cdot 10$ and $70=7\cdot10$
there will be $10^2$ when you take the product not $10^4$
hence it will have 2 zeroes not 4
How to simplify this expression??
Answer :
[tex] \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 4}{ {x}^{3} + 3 {x}^{2} + x - 1} [/tex]
Step-by-step-explanation :
I did the explanation in the picture.
Solve the following equation using the square root property.
9x2 + 10 = 5
(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability that this person i. Has a liver problems?
Answer:
The probability that the selected adult has liver problems is 0.08
Step-by-step explanation:
In this question, from the data given, we want to calculate the probability that an adult selected at random has liver problems.
Let E(L) be the event that an adult has liver problems.
The probability is directly obtainable from the question and it is given as 8%
Thus, the probability that the selected adult has liver problems; P(L) = 8% = 8/100 = 0.08
ASAP
Which of the following factors determine a plane? A. line and a point on the line B. two lines C. a straight line D. a line and a point not on that line
Answer:
D. a line and a point not on that line
Step-by-step explanation:
That is how you determine a plane.
The factors which determine a plane are a line and a point not on that line.
What is plane ?
In geometry, a plane is a flat surface that extends into infinity.
In a three dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.
Therefore, the factors which determine a plane are a line and a point not on that line.
Hence, option D is correct.
Learn more about plane here:
https://brainly.com/question/17458011
#SPJ2
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. When he started his diet, he weighed 79.5 kilograms. He gained weight at a rate of 5.5 kilograms per month. Let y represent the sumo wrestler's weight (in kilograms) after x months. Which of the following could be the graph of the relationship? graph of an increasing linear function in quadrant 1 with a positive y-intercept (Choice B) B graph of an increasing linear function in quadrants 1 and 4 with a positive x-intercept and negative y-intercept (Choice C) C graph of a decreasing linear function in quadrants 1 and 4 with a positive x-intercept and positive y-intercept (Choice D) D graph of a decreasing linear function in quadrant 4 with a negative y-intercept
Answer:
(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.
Step-by-step explanation:
The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.
If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.
So the initial weight would occur at (0, 79.5) which is the positive y-intercept.
And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.
Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.
Cheers.
Find the 14th term in the sequence 1, 1/3, 1/9, … Find the sum of the first 10 terms of the sequence above.
Answer:
This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term
Let Pn represent the nth term in the sequence
Then Pn = (1/3)^n-1
From this P14 = (1/3)^13 = 1/1594323
5. The sum of the first n terms of a GP beginning a with ratio r is given by
Sn = a* (r^n+1 - 1)/(r - 1)
With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500
What is the critical F value when the sample size for the numerator is seven and the sample size for the denominator is six
Answer:
Critical F value = 4.9503
Step-by-step explanation:
Given that:
The sample size of the numerator = 7
The sample size of the denominator = 6
The degree of freedom for the numerator df = n -1
The degree of freedom for the numerator df = 7 - 1
The degree of freedom for the numerator df = 6
The degree of freedom for the denominator df = n - 1
The degree of freedom for the denominator df = 6 - 1
The degree of freedom for the denominator df = 5
The assume that the test is two tailed and using a level of significance of ∝ = 0.10
The significance level for the two tailed test = 0.10/2 = 0.05
From the standard normal F table at the level of significance of 0.05
Critical F value = 4.9503
A laboratory tested n = 98 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 86 milligrams with σ = 7 milligrams. Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.
Answer:
1.3859
Step-by-step explanation:
The formula for Margin of Error is given as:
Margin of Error = Critical value × Standard Error
Critical value = z score
In the question, we are given a confidence interval of 95%.
Z score for a 95% confidence level is given as: 1.96
Hence, critical value = 1.96
Standard Error = σ / √n
Where n = number of samples = 98 chicken eggs
σ = Standard deviation = 7 milligrams
Standard Error = 7/√98
Standard Error = 0.7071067812
Hence, Margin of Error = Critical value × Standard Error
Margin of Error = 1.96 × 0.7071067812
Margin of Error = 1.3859292911
Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859
Solve for x. 2x+3≤x−5 x≤−8 x≤2 x≤8 x≤−2
Answer:
x≤−8
Step-by-step explanation:
2x+3≤x−5
Subtract x from each side
2x-x+3≤x-x−5
x+3≤−5
Subtract 3 from each side
x+3-3≤−5-3
x≤−8
Answer:
[tex]\huge \boxed{x \leq -8}[/tex]
Step-by-step explanation:
[tex]2x+3 \leq x-5[/tex]
[tex]\sf Subtract \ x \ from \ both \ parts.[/tex]
[tex]2x+3 -x\leq x-5-x[/tex]
[tex]\sf Simplify \ the \ inequality.[/tex]
[tex]x+3 \leq -5[/tex]
[tex]\sf Subtract \ 3 \ from \ both \ parts.[/tex]
[tex]x+3-3 \leq -5-3[/tex]
[tex]\sf Simplify \ the \ inequality.[/tex]
[tex]x \leq -8[/tex]
the coefficient of 6x
Answer:
The coefficient is 6
Step-by-step explanation:
The coefficient is the number in front of the variable
The variable is x
The coefficient is 6
Answer:
6
Step-by-step explanation: The coefficient of this would be the real number that is in front of a variable that is not a variable like x, and that number is 6. So, the coefficient of 6x is 6.
find the derivative by using product rule and distribution
pls help quickly and show work
Answer:
Below
Step-by-step explanation:
First method:
● f(x)= (x^3-2x+1)×(x-3)
● f'(x)= (x^3-2x+1)' ×(x-3) + (x^3-2x+1)×(x-3)'
●f'(x)= (3x^2-2)×(x-3) + (x^3-2x+1) × 1
●f'(x) = 3x^3-9x^2-2x+6 + x^3-2x+1
● f'(x)= 4x^3-9x^2-4x+7
■■■■■■■■■■■■■■■■■■■■■■■■■■
Second method:
●f(x) = (x^3-2x+1)×(x-3)
●f(x) = x^4-3x^3 -2x^2+6x+x-3
●f(x) = x^4-3x^3-2x^2+7x-3
●f'(x) = 4x^3-9x^2-4x+7
We got the same result using both methods.
