Test: Factors I - Ambitious

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Question 1:   Find the factors of ${x}^{3}-7x-6$
$\left(x-6\right)\left(x-1\right)\left(x+1\right)$
$\left(x-4\right)\left(x-2\right)\left(x+1\right)$
$\left(x-3\right)\left(x+2\right)\left(x+1\right)$
$\left(x+3\right)\left(x+2\right)\left(x-1\right)$
Question 2:   Find the factors of ${x}^{3}+2{x}^{2}-19x-20=0$
$\left(x-5\right)\left(x+5\right)\left(x-2\right)$
$\left(x-5\right)\left(x+4\right)\left(x-1\right)$
$\left(x-4\right)\left(x+5\right)\left(x+1\right)$
$\left(x-10\right)\left(x-2\right)\left(x+1\right)$
Question 3:   Find the factors of $2{x}^{3}+7{x}^{2}-5x-4$
$\left(2x-1\right)\left(x+1\right)\left(x+2\right)$
$2\left(x-1\right)\left(x+\frac{1}{2}\right)\left(x+4\right)$
$2\left(x-2\right)\left(x-1\right)\left(x+4\right)$
$2\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)\left(x+4\right)$
Question 4:   Find the repeated factor of ${x}^{3}-3{x}^{2}+4$
$\left(x-2\right)$
$\left(x+1\right)$
$\left(x-3\right)$
$\left(x-1\right)$
Question 5:   Find the repeated factor of ${x}^{3}-2{x}^{2}-7x-4$
$\left(x-1\right)$
$\left(x-2\frac{1}{3}\right)$
$\left(x-2\right)$
$\left(x+1\right)$
Question 6:   Find the repeated factor of $3{x}^{3}-17{x}^{2}+21+9$
$\left(x+\frac{1}{3}\right)$
$\left(x+1\right)$
$\left(x-3\right)$
$\left(x-\frac{14}{18}\right)$
Question 7:   Find the value of $k$ if $\left(x+3\right)$ is a factor of ${x}^{3}-4{x}^{2}-kx+30$
$k=2$
$k=2\frac{1}{2}$
$k=11$
$k=7$
Question 8:   Find the value of $k$ if $\left(x+\frac{1}{2}\right)$ is a factor of $6{x}^{3}-23{x}^{2}+kx+4$
$k=-8\frac{3}{7}$
$k=-7\frac{2}{3}$
$k=-13$
$k=-5$
Question 9:   Find the values of $k$ and $l$ if ${\left(x-1\right)}^{2}$ is a factor of ${x}^{3}+{x}^{2}+kx+l$
$\left\{\begin{array}{l}k=-3\\ l=5\end{array}$
$\left\{\begin{array}{l}k=-5\\ l=3\end{array}$
$\left\{\begin{array}{l}k=-2\\ l=2\end{array}$
$\left\{\begin{array}{l}k=-1\\ l=-4\end{array}$
Question 10:   Find the values of $k$ and $l$ if ${\left(x-2\right)}^{2}$ is a factor of ${x}^{3}+{x}^{2}+kx+l$
$\left\{\begin{array}{l}k=-18\\ l=22\end{array}$
$\left\{\begin{array}{l}k=-10\\ l=12\end{array}$
$\left\{\begin{array}{l}k=-8\\ l=13\end{array}$
$\left\{\begin{array}{l}k=-16\\ l=20\end{array}$