What is the identity of your unknown, how do you know? (flame test lab)

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igtguith

03.11.2021

Chemistry

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,

$6\left(-\dfrac{2}{3}\right)^3 + 3\left(-\dfrac{2}{3}\right)^2 + 4\left(-\dfrac{2}{3}\right) + 2=-\dfrac{16}{9}+\dfrac{4}{3}-\dfrac{8}{3}+2=-\dfrac{10}{9}\neq 0.$

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,

$18\left(-\dfrac{2}{3}\right)^3 -12\left(-\dfrac{2}{3}\right)^2 + 9\left(-\dfrac{2}{3}\right) -6=-\dfrac{16}{3}-\dfrac{16}{3}-6-6\neq 0.$

D. For the polynomial 21x^4 + 7x^3 + 6x + 2,

$21\left(-\dfrac{2}{3}\right)^4 +7\left(-\dfrac{2}{3}\right)^3 +6\left(-\dfrac{2}{3}\right) +2=\dfrac{112}{27}-\dfrac{56}{27}-4+2\neq 0.$

correct choice is B

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