Question

For what values of p and q ,(x+2) and (x-1) are factors of the polynomial x³+10x²+px+q.​

Answer 1

Answer:

p=7 and q=-18

Step-by-step explanation:

let f(x)=x³+10x²+px+q.

(x+2) and (x-1) are factors of f(x)

then f(-2)=0

(-2)³+10(-2)²+p(-2)+q=0

-8+40-2p+q=0

-2p+q=-32..........(1)

Also

f(1)=0

(1)³+10*(1)²+p+q=0

p+q=-11.

q=-11-p

from(1)

-2p-11-p=-32

-3p=-21

p=7

from(1) again

-14+q=-32

q=-18