Problem of the Week

Updated at Mar 29, 2021 9:12 AM

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Mar 24, 2025

How can we factor $36{n}^{2}+6n-12$ ?

Below is the solution.

36{n}^{2}+6n-12

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

36{n}^{2}

6n

, and

-12

It is

6

What is the highest degree of $n$ that divides evenly into

36{n}^{2}

6n

, and

-12

It is 1, since

n

is not in every term.

Multiplying the results above,

The GCF is

6

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GCF =

6

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

6(\frac{36{n}^{2}}{6}+\frac{6n}{6}-\frac{12}{6})

Simplify each term in parentheses.

6(6{n}^{2}+n-2)

Split the second term in

6{n}^{2}+n-2

into two terms.

Multiply the coefficient of the first term by the constant term.

6\times -2=-12

Ask: Which two numbers add up to

1

and multiply to

-12

4

and

-3

Split

n

as the sum of

4n

and

-3n

6{n}^{2}+4n-3n-2

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6(6{n}^{2}+4n-3n-2)

Factor out common terms in the first two terms, then in the last two terms.

6(2n(3n+2)-(3n+2))

Factor out the common term

3n+2

6(3n+2)(2n-1)

Done