Question

If x^3 – 2x^2 + px + q has a factor (x + 2) and leaves a remainder 9 when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely ​

Answer 1

Let,if p(x) is a factor of (x-1) and (x-2) then remainder is p(1)=0 and p(2)=0.

P(1)=1+10+p+q

         11+p+q=0-----(1)

P(-2)=-8+10(4)+(-2)p+q

          -8+40-2p+q=0

             32-2p+q=0..........(2)

Adding eq:1 and 2,

11+p+q=0

32-2p+q=0

-      +      -

-21+3p=0

3p=21

P=7

Substitute p value in equation 1

11+p+q=0

11+7+q=0

18+q=0

q=-18

P=7 and q=-18

Answer 2

Step-by-step explanation:

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