Question

What is factors of polynomial x³-4x²-11x+30?
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Answer 1

Answer:

p(x)=(x-2)(x-5)(x+3)

Step-by-step explanation:

factors of 30=±1,±2,±3,±5,±10,±15,±30

taking +2 we get

p(x)= x^3-4x^2-11x+30

=2^3-4*2^2-11×2+30

=8-16-22+30

=0

therefore (x-2)is a factor

p(x)=x^3-2x^2-2x^2+4x-15x+30

=x^2(x-2)-2x(x-2)-15(x-2)

=(x-2)(x^2-2x-15)

=(x-2)[x^2-5x+3x-15]

=(x-2)[x(x-5)+3(x-5)]

therefore p(x)=(x-2)(x-5)(x+3)