# Problem of the Week

## Updated at Sep 4, 2017 9:39 AM

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

How can we factor $$6{x}^{2}+3x-30$$?

Check out the solution below!

$6{x}^{2}+3x-30$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$6{x}^{2}$$, $$3x$$, and $$-30$$?It is $$3$$.2 What is the highest degree of $$x$$ that divides evenly into $$6{x}^{2}$$, $$3x$$, and $$-30$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$3$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$3$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$3(\frac{6{x}^{2}}{3}+\frac{3x}{3}-\frac{30}{3})$3 Simplify each term in parentheses.$3(2{x}^{2}+x-10)$4 Split the second term in $$2{x}^{2}+x-10$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times -10=-20$2 Ask: Which two numbers add up to $$1$$ and multiply to $$-20$$?$$5$$ and $$-4$$3 Split $$x$$ as the sum of $$5x$$ and $$-4x$$.$2{x}^{2}+5x-4x-10$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$3(2{x}^{2}+5x-4x-10)$5 Factor out common terms in the first two terms, then in the last two terms.$3(x(2x+5)-2(2x+5))$6 Factor out the common term $$2x+5$$.$3(2x+5)(x-2)$Done3*(2*x+5)*(x-2)