Question

( p(x)=x^{4}+p x^{3}+2 x^{2}+8 x+q )
10 ( quad ) divisible by ( x^{2}-1 )
[
begin{aligned}
p(1) &=(1)^{4}+p(1)^{3}+2(1)^{2}-3(1)+2
Rightarrow & 1+p+2-3+2
& 7 p+q=0
P(-1)=&(1)^{4}+p(-1)^{3}+2(-1)^{2}-3(-1)+2
Rightarrow & 1-P+2+3+q
& Rightarrow 6-p+q=0
end{aligned}
]
( f sigma O m(1) &(2) quad P+q )
( frac{6-p+q}{6+q=0} )
( p+q=0 )
( p-6=0 )

# 20. Find the values of p and q so that x**px42x2-3x+q la divisible by (x-1).

Solution