If binomial (3x+2) is a factor of some polynomial, then number \(x=-\dfrac{2}{3}\) is this polynomial's root. Check all polynomials:
A. For the polynomial \(6x^3 + 3x^2 + 4x + 2,\)
\(6\left(-\dfrac{2}{3}\right)^3 + 3\left(-\dfrac{2}{3}\right)^2 + 4\left(-\dfrac{2}{3}\right) + 2=-\dfrac{16}{9}+\dfrac{4}{3}-\dfrac{8}{3}+2=-\dfrac{10}{9}
eq 0.\)
B. For the polynomial \(12x^2 + 15x + 8x + 10,\)
\(12\left(-\dfrac{2}{3}\right)^2 + 23\left(-\dfrac{2}{3}\right) + 10=\dfrac{16}{3}-\dfrac{46}{3}+10=0.\)
C. For the polynomial \(18x^3-12x^2 + 9x-6,\)
\(18\left(-\dfrac{2}{3}\right)^3 -12\left(-\dfrac{2}{3}\right)^2 + 9\left(-\dfrac{2}{3}\right) -6=-\dfrac{16}{3}-\dfrac{16}{3}-6-6
eq 0.\)
D. For the polynomial \(21x^4 + 7x^3 + 6x + 2,\)
\(21\left(-\dfrac{2}{3}\right)^4 +7\left(-\dfrac{2}{3}\right)^3 +6\left(-\dfrac{2}{3}\right) +2=\dfrac{112}{27}-\dfrac{56}{27}-4+2
eq 0.\)
Answer: correct choice is B
