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Help! Identify the binomial that is a factor of the polynomial.

Help! Identify the binomial that is a factor of the polynomial.-example-1
User Bergey
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1 Answer

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The binomial that is a factor of the polynomial is (x-2).

STEP - BY - STEP EXPLANATION

What to find?

The binomial that is a factor of the polynomial.

Given:

P(x) =3x³ - 11x² -2x + 24

The factor can be determine by simply finding the zeros of the polynomial.

The zeros of a polynomial when substituted into the polynomial makes it zero.

From the given option, we shall test to see which makes the polynomial zero.

Substitute x=2 into the given polynomial and simplify.

That is;

p(3) = 3(2)³ - 11(2)² -2(2)+ 24

=3(8) - 11(4) - 2(2) + 24

=24 - 44 - 4 + 24

=0

Hence, p(x) = 0 when x=2.

This implies x-2 is a factor of the polynomial.

Since x=2 is the only digit among the option that makes p(x) =0, then (x-2) is the only binomial that is a factor among the options given.

User Blake Miller
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