hionormf

2021-12-14

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

Jim Hunt

Beginner2021-12-15Added 45 answers

Step 1

Consider the polynomials

(a)${x}^{2}-8x$

(b)${x}^{3}+3{x}^{2}-18x$

(c)${x}^{3}-10x$

Step 2

(a)${x}^{2}-8x$

${x}^{2}-8x=x(x-8)$

Step 3

(b)${x}^{3}+3{x}^{2}-18x$

${x}^{3}+3{x}^{2}-18x=x({x}^{2}+3x-18)$

$=x({x}^{2}+6x-3x-18)$

=x(x(x+6)-3(x+6))

=x((x+6)(x-3))

=x(x+6)(x-3)

${x}^{3}+3{x}^{2}-18x=x(x+6)(x-3)$

Step 4

(c)${x}^{3}-10x$

${x}^{3}-10x=x({x}^{2}-10)$

Consider the polynomials

(a)

(b)

(c)

Step 2

(a)

Step 3

(b)

=x(x(x+6)-3(x+6))

=x((x+6)(x-3))

=x(x+6)(x-3)

Step 4

(c)

Debbie Moore

Beginner2021-12-16Added 43 answers

(a)${x}^{2}-8x=x(x-8)$

After factoring out x we have:

${x}^{2}-8x=x(x-8)$

(b)${x}^{3}+3{x}^{2}-18x=x(x-3)(x+6)$

Explanation:

After factoring out x we have:

${x}^{3}+3{x}^{2}-18x=x({x}^{2}+3x-18)$

(c)${x}^{3}-10x=x({x}^{2}-10)$

After factoring out x we have:

${x}^{3}-10x=x({x}^{2}-10)$

After factoring out x we have:

(b)

Explanation:

After factoring out x we have:

(c)

After factoring out x we have:

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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