Use the remainder theorem and the factor theorem to determine which of the following binomials are factors of p(x)=x^3-8x^2+5x+14

Try if (x+1) is a factor of p(x)

P(-1)=(-1)^3-8*(-1)^2+5*(-1)+14=-1-8-5+14=0

So (x+1) is a factor of p(x), and x=-1 is a root of p(x)

p(x)=x^3-8x^2+5x+14

=x^2(x+1)-x^2-8x^2+5x+14

=x^2(x+1)-9x(x+1)+9x+5x+14

=x^2(x+1)-9x(x+1)+14(x+1)

=(x+1)(x^2-9x+14)

=(x+1)(x-7)(x-2)

So (x+1), (x-7), and (x-2) are factors of p(x)=x^3-8x^2+5x+14

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