Problem of the Week

Updated at May 17, 2021 11:07 AM

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May 5, 2025

How would you find the factors of $30{v}^{2}-24v-6$ ?

Below is the solution.

30{v}^{2}-24v-6

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

30{v}^{2}

-24v

, and

-6

It is

6

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

30{v}^{2}

-24v

, and

-6

It is 1, since

v

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{30{v}^{2}}{6}+\frac{-24v}{6}-\frac{6}{6})

Simplify each term in parentheses.

6(5{v}^{2}-4v-1)

Split the second term in

5{v}^{2}-4v-1

into two terms.

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

5\times -1=-5

Ask: Which two numbers add up to

-4

and multiply to

-5

1

and

-5

Split

-4v

as the sum of

v

and

-5v

5{v}^{2}+v-5v-1

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6(5{v}^{2}+v-5v-1)

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

6(v(5v+1)-(5v+1))

Factor out the common term

5v+1

6(5v+1)(v-1)

Done