# Problem of the Week

## Updated at Oct 29, 2018 9:27 AM

How can we factor $$6{x}^{2}+33x-18$$?

Below is the solution.

$6{x}^{2}+33x-18$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$6{x}^{2}$$, $$33x$$, and $$-18$$?It is $$3$$.2 What is the highest degree of $$x$$ that divides evenly into $$6{x}^{2}$$, $$33x$$, and $$-18$$?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{33x}{3}-\frac{18}{3})$3 Simplify each term in parentheses.$3(2{x}^{2}+11x-6)$4 Split the second term in $$2{x}^{2}+11x-6$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times -6=-12$2 Ask: Which two numbers add up to $$11$$ and multiply to $$-12$$?$$12$$ and $$-1$$3 Split $$11x$$ as the sum of $$12x$$ and $$-x$$.$2{x}^{2}+12x-x-6$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$3(2{x}^{2}+12x-x-6)$5 Factor out common terms in the first two terms, then in the last two terms.$3(2x(x+6)-(x+6))$6 Factor out the common term $$x+6$$.$3(x+6)(2x-1)$Done3*(x+6)*(2*x-1)