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Question

If (x+2) and (x-1) are factors of the polynomial p(x)=x3+10x2+mx+n then
(a) m=5,n=3
(b) m=7,n=18
(c) m=17,n=8
(d) m=23,n=19

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Solution

ANSWER:
(b) m = 7, n = −18
Let:
px=x3+10x2+mx+n
Now,
x+2=0⇒x=-2
(x + 2) is a factor of p(x).
So, we have p(-2)=0
⇒-23+10×-22+m×-2+n=0⇒-8+40-2m+n=0⇒32-2m+n=0⇒2m-n=32 ...i
Now,

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