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Question
Factorise x3−10x2−53x−42, using factor theorem.
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Solution
x3−10x2−53x−42
let p(x)=x3−10x2−53x−42
let x=−1
p(−1)=(−1)3−10(−1)2−53(−1)−42
=−1−10+53−42
=0
Hence (x+1) is factor of polynomial
p(x)=x3+x2−11x2−42x−11x−42
⇒x2(x+1)−11x(x+1)−42(x+1)
⇒(x+1)(x2−11x−42)
x2−11x−42=x2−14x+3x−42
=x(x−14)+3(x−14)
=(x+3)(x−14)
∴p(x)=(x+1)(x+3)(x−14)
let p(x)=x3−10x2−53x−42
let x=−1
p(−1)=(−1)3−10(−1)2−53(−1)−42
=−1−10+53−42
=0
Hence (x+1) is factor of polynomial
p(x)=x3+x2−11x2−42x−11x−42
⇒x2(x+1)−11x(x+1)−42(x+1)
⇒(x+1)(x2−11x−42)
x2−11x−42=x2−14x+3x−42
=x(x−14)+3(x−14)
=(x+3)(x−14)
∴p(x)=(x+1)(x+3)(x−14)
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