Question

Check whether 7 + 3x is a factor of 3x3 + 7x.​

Answer 1

Answer:

$3x^3+7x=7+3x\quad :\quad x=1,\:x=-\frac{1}{2}+i\frac{5\sqrt{3}}{6},\:x=-\frac{1}{2}-i\frac{5\sqrt{3}}{6}$

No 7+3x is not the factor of 3x³ + 7x

Step-by-step explanation:

$\left(3\left(-\frac{1}{2}\right)-i\frac{5\sqrt{3}}{6}\right)^3+7\left(-\frac{1}{2}\right)-i\frac{5\sqrt{3}}{6}=\frac{5}{2}-i\frac{85\sqrt{3}}{18}$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=\left(-3\times \frac{1}{2}-i\frac{5\sqrt{3}}{6}\right)^3-7\times \frac{1}{2}-i\frac{5\sqrt{3}}{6}$

$=\left(-\frac{5\sqrt{3}i}{6}-\frac{3}{2}\right)^3-\frac{7}{2}-\frac{5\sqrt{3}i}{6}$

$=\frac{75}{8}+\frac{-81\sqrt{3}-280i}{24\sqrt{3}}-\frac{7}{2}-\frac{5\sqrt{3}i}{6}$

$=\frac{47}{8}+\frac{-340i-81\sqrt{3}}{24\sqrt{3}}$

$=\frac{47}{8}+\frac{-243-340\sqrt{3}i}{72}$

$=\frac{5}{2}-\frac{85\sqrt{3}}{18}i$

HOPE IT HELPS YOU

Eva*