# Problem of the Week

## Updated at May 24, 2021 12:47 PM

How can we compute the factors of $$4{z}^{2}+6z-4$$?

Below is the solution.

$4{z}^{2}+6z-4$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$4{z}^{2}$$, $$6z$$, and $$-4$$?It is $$2$$.2 What is the highest degree of $$z$$ that divides evenly into $$4{z}^{2}$$, $$6z$$, and $$-4$$?It is 1, since $$z$$ 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{4{z}^{2}}{2}+\frac{6z}{2}-\frac{4}{2})$3 Simplify each term in parentheses.$2(2{z}^{2}+3z-2)$4 Split the second term in $$2{z}^{2}+3z-2$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times -2=-4$2 Ask: Which two numbers add up to $$3$$ and multiply to $$-4$$?$$4$$ and $$-1$$3 Split $$3z$$ as the sum of $$4z$$ and $$-z$$.$2{z}^{2}+4z-z-2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(2{z}^{2}+4z-z-2)$5 Factor out common terms in the first two terms, then in the last two terms.$2(2z(z+2)-(z+2))$6 Factor out the common term $$z+2$$.$2(z+2)(2z-1)$Done2*(z+2)*(2*z-1)