Where is the moon located in relation to Earth and the sun when it is a first-quarter moon? (1 point) behind Earth and away from the sun
behind Earth and away from the sun

perpendicular to Earth and the sun
perpendicular to Earth and the sun

behind the sun and away from Earth
behind the sun and away from Earth

between Earth and the sun

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Ответ:

paulusl19

16.07.2020

Mathematics

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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