Problem of the Week

Updated at Oct 1, 2018 9:52 AM

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Mar 24, 2025

How would you find the factors of $15{p}^{2}-45p+30$ ?

Below is the solution.

15{p}^{2}-45p+30

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

15{p}^{2}

-45p

, and

30

It is

15

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

15{p}^{2}

-45p

, and

30

It is 1, since

p

is not in every term.

Multiplying the results above,

The GCF is

15

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GCF =

15

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

15(\frac{15{p}^{2}}{15}+\frac{-45p}{15}+\frac{30}{15})

Simplify each term in parentheses.

15({p}^{2}-3p+2)

Factor

{p}^{2}-3p+2

Ask: Which two numbers add up to

-3

and multiply to

2

-2

and

-1

Rewrite the expression using the above.

(p-2)(p-1)

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15(p-2)(p-1)

Done