Question

(x+2)(x-3)(x+5) is identical to x^3+ax^2-11x+b what are a and b

Answer 1

$\textbf{Given:}$

$(x+2)(x-3)(x+5){\equiv}x^3+a\,x^2-11\,x+b$

$\textbf{To find:}$

$\text{The values of a and b}$

$\textbf{Solution:}$

$\text{Consider,}$

$(x+2)(x-3)(x+5){\equiv}x^3+a\,x^2-11\,x+b$

$x^3-(-2+3-5)x^2+(3(-2)+3(-5)+(-5)(-2))x-((-2)3(-5)){\equiv}x^3+a\,x^2-11\,x+b$

$x^3-(-4)x^2+(-6-15+10)x-(3(10)){\equiv}x^3+a\,x^2-11\,x+b$

$x^3+4x^2-11x-30{\equiv}x^3+a\,x^2-11\,x+b$

$\text{Comparing corresponding coefficients on bothsides, we get}$

$a=4\;\text{and}\;b=-30$

$\textbf{Answer:}$

$\boxed{\bf\,a=4\,\textbf{and}\;b=-30}$

Answer 2

Answer:

a = 4 and b = - 30

Step-by-step explanation:

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