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Mathematics
06.12.2021 09:48
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Jennie ran the first 6 miles of a marathon in 58 minutes. If she is able to maintain

Jennie ran the first 6 miles of a marathon in 58 minutes. If she is able to maintain the same pace, how long will it take her to finish the 26.2 miles?
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bluebug7316
bluebug7316
4,5(13 marks)

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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