# Problem of the Week

## Updated at Jun 25, 2018 11:17 AM

How can we compute the factors of $$10{x}^{2}-35x+25$$?

Below is the solution.

$10{x}^{2}-35x+25$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$10{x}^{2}$$, $$-35x$$, and $$25$$?It is $$5$$.2 What is the highest degree of $$x$$ that divides evenly into $$10{x}^{2}$$, $$-35x$$, and $$25$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$5$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$5$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$5(\frac{10{x}^{2}}{5}+\frac{-35x}{5}+\frac{25}{5})$3 Simplify each term in parentheses.$5(2{x}^{2}-7x+5)$4 Split the second term in $$2{x}^{2}-7x+5$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times 5=10$2 Ask: Which two numbers add up to $$-7$$ and multiply to $$10$$?$$-2$$ and $$-5$$3 Split $$-7x$$ as the sum of $$-2x$$ and $$-5x$$.$2{x}^{2}-2x-5x+5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$5(2{x}^{2}-2x-5x+5)$5 Factor out common terms in the first two terms, then in the last two terms.$5(2x(x-1)-5(x-1))$6 Factor out the common term $$x-1$$.$5(x-1)(2x-5)$Done 5*(x-1)*(2*x-5)