Which polynomial has (3x+2) as a binomial factor? 6x^3+3x^2+4x+2 12x^2+15x+8x+10 18x^3-12x^2+9x-6 21x^4+7x^3+6x+2

Question

Answer 1

To determine which polynomial has

as a binomial factor, we can use polynomial division or synthetic division. Let's perform synthetic division for each polynomial to see which one has

as a factor.### Polynomial 1:

Let's divide by

using synthetic division:1. Rewrite

as

.2. Use

for synthetic division.```-2 | 6 3 4 2 | -12 18 -28 ------------------- 6 -9 22 -26```The remainder is not zero, so

is not a factor of

.### Polynomial 2:

This polynomial is not correctly written. Let's assume it is

.Let's divide by

using synthetic division:```-2 | 12 23 10 | -24 -14 ------------------- 12 -1 -4```The remainder is not zero, so

is not a factor of

.### Polynomial 3:

Let's divide by

using synthetic division:```-2 | 18 -12 9 -6 | -36 96 -174 ------------------- 18 -48 105 -180```The remainder is not zero, so

is not a factor of

.### Polynomial 4:

Let's divide by

using synthetic division:```-2 | 21 7 0 6 2 | -42 -14 28 -108 ----------------------- 21 -35 14 34 -106```The remainder is not zero, so

is not a factor of

.None of the given polynomials have

as a binomial factor.

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