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
Answers
Answer:
If binomial (3x+2) is a factor of some polynomial, then number x=-\dfrac{2}{3}x=−
3
2
is this polynomial's root. Check all polynomials:
A. For the polynomial 6x^3 + 3x^2 + 4x + 2,6x
3
+3x
2
+4x+2,
6(-\dfrac{2}{3})^3 + 3(-\dfrac{2}{3})^2 + 4(-\dfrac{2}{3}) + 2=-\dfrac{16}{9}+\dfrac{4}{3}-\dfrac{8}{3}+2=-\dfrac{10}{9}\neq 0.6(−
3
2
)
3
+3(−
3
2
)
2
+4(−
3
2
)+2=−
9
16
+
3
4
−
3
8
+2=−
9
10
=0.
B. For the polynomial 12x^2 + 15x + 8x + 10,12x
2
+15x+8x+10,
12(-\dfrac{2}{3})^2 + 23(-\dfrac{2}{3}) + 10=\dfrac{16}{3}-\dfrac{46}{3}+10=0.12(−
3
2
)
2
+23(−
3
2
)+10=
3
16
−
3
46
+10=0.
C. For the polynomial 18x^3-12x^2 + 9x-6,18x
3
−12x
2
+9x−6,
18(-\dfrac{2}{3})^3 -12(-\dfrac{2}{3})^2 + 9(-\dfrac{2}{3}) -6=-\dfrac{16}{3}-\dfrac{16}{3}-6-6\neq 0.18(−
3
2
)
3
−12(−
3
2
)
2
+9(−
3
2
)−6=−
3
16
−
3
16
−6−6
=0.
D. For the polynomial 21x^4 + 7x^3 + 6x + 2,21x
4
+7x
3
+6x+2,
21(-\dfrac{2}{3})^4 +7(-\dfrac{2}{3})^3 +6(-\dfrac{2}{3}) +2=\dfrac{112}{27}-\dfrac{56}{27}-4+2\neq 0.21(−
3
2
)
4
+7(−
3
2
)
3
+6(−
3
2
)+2=
27
112
−
27
56
−4+2
=0.
Answer: correct choice is B
thanks