Question

if the polynomial x^3+2x^2+ax+b has factors (x+1) and (x-1), find the value of a and b

Answer 1

(x-1) and (x+1) are factors of the given polynomial.

x-1 = 0. ; x+1 = 0

x = 1. ; x = -1

Put x= -1,1 to find a and b

First,put x = 1

x³+2x²+ax+b = 0

(1)³+2(1)²+a(1)+b = 0

1+2(1)+a+b = 0

1+2+a+b = 0

a+b+3 = 0

a+b = -3 -------(1)

Put x = -1,

(-1)³+2(-1)²+a(-1)+b = 0

-1+2(1)-a+b = 0

-1+2-a+b = 0

-a+b+1 = 0

-a+b = -1 ------(2)

(1)+(2)

a+b = -3
-a+b = -1
------------
2b = -4

b = -4/2

b = -2

Put b=-2 in (1)

a+(-2) = -3

a-2 = -3

a=-3+2

a = -1

Therefore, a = -1 and b = -2