# Problem of the Week

## Updated at Dec 25, 2017 9:49 AM

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

How would you find the factors of $$14{x}^{2}-42x+28$$?

Check out the solution below!

$14{x}^{2}-42x+28$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$14{x}^{2}$$, $$-42x$$, and $$28$$?It is $$14$$.2 What is the highest degree of $$x$$ that divides evenly into $$14{x}^{2}$$, $$-42x$$, and $$28$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$14$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$14$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$14(\frac{14{x}^{2}}{14}+\frac{-42x}{14}+\frac{28}{14})$3 Simplify each term in parentheses.$14({x}^{2}-3x+2)$4 Factor $${x}^{2}-3x+2$$.1 Ask: Which two numbers add up to $$-3$$ and multiply to $$2$$?$$-2$$ and $$-1$$2 Rewrite the expression using the above.$(x-2)(x-1)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$14(x-2)(x-1)$Done14*(x-2)*(x-1)