# Test: Factors I - Challenging

Double click on maths expressions to zoom
Question 1:   Factorise: $7{x}^{3}-8{x}^{2}+5x=...$
$x\left(7{x}^{2}-8x+5\right)$
$\frac{x}{7}\left(x-\frac{5}{7}\right)\left(x-\frac{3}{5}\right)$
$x\left(7{x}^{2}-x+5\text{\hspace{0.17em}}\right)$
$x\left({x}^{2}-8x+5\text{\hspace{0.17em}}\right)$
Question 2:   Factorise: ${x}^{3}-8{x}^{2}+19x-12=...$
$\left(x-1\right)\left(x-3\right)\left(x-4\right)$
$\left(x-1\right)\left(x-2\right)\left(x-4\right)$
$\left(x-1\right)\left({x}^{2}-x+12\right)$
$\left(x-1\right)\left({x}^{2}-7x+12\right)$
Question 3:   Factorise: $\left({x}^{2}+x+3\right)\left({x}^{2}+x+4\right)-12$
$x\left(x+1\right)\left({x}^{2}+x+7\right)$
$\left({x}^{2}+x\right)\left({x}^{2}+x+7\right)$
$x\left(x+1\right)\left(x+7\right)\left(x-1\right)$
$x\left(x+1\right)\left({x}^{2}+x+6\right)$
Question 4:   Factorise: ${\left(2x-1\right)}^{4}-{\left(x+1\right)}^{4}=...$
$\left(3{x}^{2}-6x\right)\left(5{x}^{2}-2x+2\right)$
$\left({\left(2x-1\right)}^{2}-{\left(x+1\right)}^{2}\right)×\left({\left(2x-1\right)}^{2}+{\left(x+1\right)}^{2}\right)$
$3x\left(x-2\right)\left(5{x}^{2}-2x+2\right)$
$\left({\left(2x-1\right)}^{2}-{\left(x+1\right)}^{2}\right)×\left({\left(2x-1\right)}^{2}+{\left(x+1\right)}^{2}\right)$
Question 5:   Factorise: ${x}^{3}-7{x}^{2}+15x-9=...$.
${\left(x-1\right)}^{2}\left(x-3\right)$
$\left(x-1\right){\left(x-3\right)}^{2}$
$\left(x-1\right)\left(x-2\right)\left(x-3\right)$
$\left(x-1\right)\left({x}^{2}-6x+9\right)$
Question 6:   Factorise: $16{x}^{4}-8{x}^{2}+1=...$
${\left(4{x}^{2}-1\right)}^{2}$
${\left(2x-1\right)}^{2}{\left(2x+1\right)}^{2}$
${\left(x-1\right)}^{2}{\left(2x+1\right)}^{2}$
${\left(x-1\right)}^{2}{\left(x+1\right)}^{2}$
Question 7:   Factorise: $3{x}^{2}y+2{y}^{2}+3{x}^{3}+2xy=...$
$3{x}^{2}\left(y+x\right)+2y\left(y+x\right)$
$\left(x+y\right)\left(3{x}^{2}+y\right)$
$\left(x+y\right)\left(3x+2y\right)$
$\left(x+y\right)\left(3{x}^{2}+2y\right)$
Question 8:   Factorise: $2{x}^{2}-7x-3=...$
$\left(x-3\right)\left(x-\frac{1}{2}\right)$
$2\left(x-3\right)\left(x-\frac{1}{2}\right)$
$2\left(x-1\right)\left(x-\frac{1}{2}\right)$
$\left(x-3\right)\left(x-1\right)\right)$
Question 9:   Reduce: $\frac{9{x}^{2}-6x+1}{3x-1}=...$
$\frac{1}{3x-1}$
$x$
$1$
$3x-1$
Question 10:   Reduce: $\frac{{x}^{3}-2{x}^{2}+2x}{x-2}=...$
$1$
$2x\left(x-1\right)$
$\frac{1}{x-2}$
$\frac{x\left({x}^{2}-2x+2\right)}{x-1}$