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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

User Mullefa
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2 Answers

4 votes

Answer:

B 12x2 + 15x + 8x + 10

Explanation:

Did it

User Roque
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7.8k points
0 votes

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

User SirC
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8.5k points