How do you factor z squared plus 7z plus 6?

Answer 1

The procedure for factoring

z2+7z+6

is as follows:

First, we must look at the number in front of the first variable. In this case, it is a 1. Then we look at the last number in the expression, which is a 6 (the expression must be arranged in descending order by the exponents of the variables).

Now, we multiply these two numbers together.

1 x 6 = 6

We need to factors of 6 that when added together equal 7. The factors of 6 are as follows

1 x 6

2 x 3

The first set of factors is the only set that adds up to equal 7. So now we break apart the middle term into 1 and 6, so that it looks like this:

z2+z+6z+6

Now we group the expression like this

(z2+z)+(6z+6)

With the parenthesis like this, we can begin pulling out common factors, leaving the expression looking like this

z(z+1)+6(z+1)

Because the contents of the sets of parenthesis are the same, we can combine the z and the 6 to get the fully-factored expression

(z+6)(z+1)