Question

If a polynomial x4 +7 x3 + 7x2 + px +q is exactly divisible by x2 + 7x + 12, then find the value of p and q.

Answer 1

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Answer 2

Solution:

Let p(x) = x⁴+7x³+7x²+px+q

g(x) = x²+7x+12

It is given that, p(x) is exactly

divisible by g(x)

g(x)|x⁴+7x³+7x²+px+q|x²-5

****x⁴+7x³+12x²

_____________________

********** -5x²+px+q

********** -5x²-35x-60

_______________________

Remainder [(p+35)x+(q+60)]

According to the problem given,

p(x) is exactly divisible by g(x),

Remainder = 0

=> p+35 = 0 and q+60 = 0

=> p = -35 and q = -60

Therefore,

p = -35 , q = -60

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