Question

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

Answer 1

B 12x2 + 15x + 8x + 10

Explanation:

Did it

Answer 2

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