# Problem of the Week

## Updated at Oct 1, 2018 9:52 AM

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

Below is the solution.

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

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$15{p}^{2}$$, $$-45p$$, and $$30$$?It is $$15$$.2 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.3 Multiplying the results above,The GCF is $$15$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$15$$2 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})$3 Simplify each term in parentheses.$15({p}^{2}-3p+2)$4 Factor $${p}^{2}-3p+2$$.1 Ask: Which two numbers add up to $$-3$$ and multiply to $$2$$?$$-2$$ and $$-1$$2 Rewrite the expression using the above.$(p-2)(p-1)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$15(p-2)(p-1)$Done 15*(p-2)*(p-1)