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)
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