Problem of the Week

Updated at Jun 18, 2018 8:31 AM

For this week we've brought you this algebra problem.

How would you find the factors of $$15{x}^{2}-20x+5$$?

Here are the steps:

$15{x}^{2}-20x+5$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$15{x}^{2}$$, $$-20x$$, and $$5$$?It is $$5$$.2 What is the highest degree of $$x$$ that divides evenly into $$15{x}^{2}$$, $$-20x$$, and $$5$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$5$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$5$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$5(\frac{15{x}^{2}}{5}+\frac{-20x}{5}+\frac{5}{5})$3 Simplify each term in parentheses.$5(3{x}^{2}-4x+1)$4 Split the second term in $$3{x}^{2}-4x+1$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$3\times 1=3$2 Ask: Which two numbers add up to $$-4$$ and multiply to $$3$$?$$-1$$ and $$-3$$3 Split $$-4x$$ as the sum of $$-x$$ and $$-3x$$.$3{x}^{2}-x-3x+1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$5(3{x}^{2}-x-3x+1)$5 Factor out common terms in the first two terms, then in the last two terms.$5(x(3x-1)-(3x-1))$6 Factor out the common term $$3x-1$$.$5(3x-1)(x-1)$Done5*(3*x-1)*(x-1)