find the values of a and b so that the polynomial x³-10x²+ax+b is exactly divisible by (x-2) and (x-3)?
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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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