Question

Polynomial x^4 + 7x^3 + 7x^2 + px + q is exactly divisible by x^2 + 7x + 12, then find the value of p and q.

Answer 1

they've given it exactly divdes
so remainder =0
see above
p=-35and q=-60

Answer 2

Polynomial x4+7x3+px+q is exactly divisible by x2+7x+12.The remainder when x4+7x3+px+q is divisible by x2+7x+12 is zero
Remainder=(p+35)x+(q+60)i.e, p+35=0⇒p=−35 andq+60=0⇒q=−60Hence the values of p and q are −35 and −60 respectively.
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