Question

Factor the polynomial COMPLETELY! show ALL work please!
`3x^(3) + 6x^(2) + 3x`

Answer 1

`\because3x^3+6x^2+3x`

→ To factorize it we must find the greatest common factor of the 3 terms

∵ The common factor of 3, 6, and 3 is 3

∵ The common factor of x^3, x^2, and x is x

∴ The greatest common factor of the 3 terms is 3x

→ Divide each term by 3x

`\because(3x^3)/(3x)=x^2`
`\because(6x^2)/(3x)=2x`
`\because(3x)/(3x)=1`

`\therefore3x^3+6x^2+3x=3x(x^2+2x+1)`

→ Now we must factorize the bracket into two factors

`\begin{gathered} \because x^2=x* x \\ \because1=1*1 \\ \because(x)(1)+(x)(1)=2x \end{gathered}`
`\therefore x^2+2x+1=(x+1)(x+1)`

∴ The complete factorization is

`3x^3+6x^2+3x=3x(x+1)(x+1)=3x(x+1)^2`