Mathematics High School

if x^3+ax^2-18x+b = (x+5)(x-4)(x+2) what is a and b

Answers

Answer 1

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[tex] (x + 5)(x - 4)(x + 2) = [/tex]

[tex](x + 5) ({x}^{2} - 2x - 8) = [/tex]

[tex] {x}^{3} - 2 {x}^{2} - 8x + 5 {x}^{2} - 10x - 40 = \\ [/tex]

[tex] {x}^{3} + 3 {x}^{2} - 18x - 40[/tex]

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Compare :

[tex] {x}^{3} + 3 {x}^{2} - 18x - 40[/tex]

[tex] {x}^{3} + a {x}^{2} - 18x + b[/tex]

Thus :

[tex]a = 3[/tex]

and

[tex]b = - 40[/tex]

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