# Problem of the Week

## Updated at May 28, 2018 10:29 AM

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

How can we compute the factors of $$2{x}^{2}-10x-28$$?

Check out the solution below!

$2{x}^{2}-10x-28$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$2{x}^{2}$$, $$-10x$$, and $$-28$$?It is $$2$$.2 What is the highest degree of $$x$$ that divides evenly into $$2{x}^{2}$$, $$-10x$$, and $$-28$$?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{2{x}^{2}}{2}+\frac{-10x}{2}-\frac{28}{2})$3 Simplify each term in parentheses.$2({x}^{2}-5x-14)$4 Factor $${x}^{2}-5x-14$$.1 Ask: Which two numbers add up to $$-5$$ and multiply to $$-14$$?$$-7$$ and $$2$$2 Rewrite the expression using the above.$(x-7)(x+2)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(x-7)(x+2)$Done2*(x-7)*(x+2)