hionormf

2021-12-14

Factor the following polynomials. (a)${x}^{2}-8x$ (b)${x}^{3}+3{x}^{2}-18x$ (c) ${x}^{3}-10x$

### Answer & Explanation

Jim Hunt

Step 1
Consider the polynomials
(a)${x}^{2}-8x$
(b)${x}^{3}+3{x}^{2}-18x$
(c)${x}^{3}-10x$
Step 2
(a)${x}^{2}-8x$
${x}^{2}-8x=x\left(x-8\right)$
Step 3
(b)${x}^{3}+3{x}^{2}-18x$
${x}^{3}+3{x}^{2}-18x=x\left({x}^{2}+3x-18\right)$
$=x\left({x}^{2}+6x-3x-18\right)$
=x(x(x+6)-3(x+6))
=x((x+6)(x-3))
=x(x+6)(x-3)
${x}^{3}+3{x}^{2}-18x=x\left(x+6\right)\left(x-3\right)$
Step 4
(c)${x}^{3}-10x$
${x}^{3}-10x=x\left({x}^{2}-10\right)$

Debbie Moore

(a)${x}^{2}-8x=x\left(x-8\right)$
After factoring out x we have:
${x}^{2}-8x=x\left(x-8\right)$
(b)${x}^{3}+3{x}^{2}-18x=x\left(x-3\right)\left(x+6\right)$
Explanation:
After factoring out x we have:
${x}^{3}+3{x}^{2}-18x=x\left({x}^{2}+3x-18\right)$
(c)${x}^{3}-10x=x\left({x}^{2}-10\right)$
After factoring out x we have:
${x}^{3}-10x=x\left({x}^{2}-10\right)$

Do you have a similar question?

Recalculate according to your conditions!