Question

Find the value of p and q so that ( x +1 ) and ( x - 1 ) arr the factors of the polynomial x^4 + px^3 + 2x^2 - 3x +q

Answer 1

Given polynomial,
x^4+px³+2x²-3x+q
x+1 is one of the factor.
x+1=0
x= -1

put x= -1 in given polynomial
(-1)^4+p(-1)³+2(-1)²-3(-1)+q=0
. 1+p(-1)+2(1)+3+q=0
1-p+2+3+q=0
-p+q+6=0
-p+q=-6
-(p-q) =-(6)
p-q=6

x-1 is also one of the factor.
x-1=0
x=1

put x=1 in given polynomial
(1)^4+p(1)³+2(1)²-3(1)+q=0
1+p+2-3+q=0
p+q+0=0
p+q=0

p-q=6
p+q=0
————
2p=6
p=6/2
p=3

p+q=0
3+q=0
q=-3

p=3,q= -3

hope it helps you