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