# Problem of the Week

## Updated at Jun 29, 2020 2:29 PM

To get more practice in algebra, we brought you this problem of the week:

How can we compute the factors of $$30{x}^{2}-44x+16$$?

Check out the solution below!

$30{x}^{2}-44x+16$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$30{x}^{2}$$, $$-44x$$, and $$16$$?It is $$2$$.2 What is the highest degree of $$x$$ that divides evenly into $$30{x}^{2}$$, $$-44x$$, and $$16$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$2$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$2$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$2(\frac{30{x}^{2}}{2}+\frac{-44x}{2}+\frac{16}{2})$3 Simplify each term in parentheses.$2(15{x}^{2}-22x+8)$4 Split the second term in $$15{x}^{2}-22x+8$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$15\times 8=120$2 Ask: Which two numbers add up to $$-22$$ and multiply to $$120$$?$$-10$$ and $$-12$$3 Split $$-22x$$ as the sum of $$-10x$$ and $$-12x$$.$15{x}^{2}-10x-12x+8$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(15{x}^{2}-10x-12x+8)$5 Factor out common terms in the first two terms, then in the last two terms.$2(5x(3x-2)-4(3x-2))$6 Factor out the common term $$3x-2$$.$2(3x-2)(5x-4)$Done 2*(3*x-2)*(5*x-4)