Question

If(x+1)and(x-1) are factors of p(x)=ax^3+x^2-2x+b,find the value of a and b

Answer 1

p(x)= ax³+x²-2x+b
x+1=0, x= -1
p(-1)= a(-1)³+(-1)²-2(-1)+b
0= -a+1+2+b
a-b=3 ------> Eq1
p(1)= a(1)³+(1)²-2(1)+b
0= a+1-2+b
a+ b = 1 --------> Eq2
From Eq1&Eq2
a - b = 3
a + b = 1
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2a = 4
a=2
Sub a=2 in Eq2
2+ b = 1
b = -1