Question

For what values of a and b so that the polynomial x
3
+10x
2
+ax+b is exactly divisible by (x−1) and (x+2).

Answer 1

Answer:

Here's your answer

x

3

−10x

2

+ax+b=f(x)

if f(x) is divisible by (x−1) and (x−2)

⇒f(1)=0=f(2)

f(1)=1−10+a+b=0⇒a+b=9

f(2)=8−40+2a+b=0⇒2a+b=32

∴a=23 b=−14

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