Question

Find the polynomial p(x) of degree 4,which has x2-3x+2 as a factor and also given that p(-1)=24,p(-2)=132 and p(0)=2​

Answer 1

Answer:$p(x) =(x-1)(x-2)(2x^2-x+1)$

Step-by-step explanation:

1) Since, $(x^2-3x+2)$ is a factor of p(x) .

Therefore,

$p(x) = a(x^2+bx+c)(x^2-3x+2)$

2) Then, we have

$p(0) = 2\\ \\=> 2*a*c =2$

$p(-2) = 132 \\ \\ => 12a(4-2b+c) = 132$

$p(-1)= 6a(1-b+c)=24$

3) Then, on solving these equations

$1-b=3c\\ 2-b= 5c$

Then, we get

c= 1/2 , b = -1/2

On substitution,

a = 2 .

Hence,

$p(x) =(x-1)(x-2)(2x^2-x+1)$