Which polynomial has (3x + 2) as a binomial factor? 6x3 + 3x2 + 4x + 2 12x2 + 15x + 8x + 10 18x3 – 12x2 + 9x – 6 21x4 + 7x3 + 6x + 2

Question

asked Sep 24, 2018 208k views

2 Answers

SirC · Answer 1 · 2018-09-30T18:32:34+0000

If binomial (3x+2) is a factor of some polynomial, then number
x=-(2)/(3) is this polynomial's root. Check all polynomials:

A. For the polynomial
6x^3 + 3x^2 + 4x + 2,

$6\left(-(2)/(3)\right)^3 + 3\left(-(2)/(3)\right)^2 + 4\left(-(2)/(3)\right) + 2=-(16)/(9)+(4)/(3)-(8)/(3)+2=-(10)/(9)\\eq 0.$

B. For the polynomial
12x^2 + 15x + 8x + 10,

$12\left(-(2)/(3)\right)^2 + 23\left(-(2)/(3)\right) + 10=(16)/(3)-(46)/(3)+10=0.$

C. For the polynomial
18x^3-12x^2 + 9x-6,

$18\left(-(2)/(3)\right)^3 -12\left(-(2)/(3)\right)^2 + 9\left(-(2)/(3)\right) -6=-(16)/(3)-(16)/(3)-6-6\\eq 0.$

D. For the polynomial
21x^4 + 7x^3 + 6x + 2,

$21\left(-(2)/(3)\right)^4 +7\left(-(2)/(3)\right)^3 +6\left(-(2)/(3)\right) +2=(112)/(27)-(56)/(27)-4+2\\eq 0.$

Answer: correct choice is B