How to factor x^2+20x+19

Factoring means we want something like

(x+_) (x+_)

We will need two numbers that add together to get 20, and multiply together to get 19.

I chose 1 and 19

1+19=20 and 1*19=19

fill in the blanks

Answer: (x+1) (x+19)

First, you have to list out all the factors of the number on the right hand side, which is the one without the x, or any variables. In this case, it should be 19, so the factors of 19 are 1 and 19.

Next, determine which factors can add up or subtract to the number in the middle, which is 20 in this case. Since the only factors of 19 are 1 and 19, they're the only one that can make up 20 by adding them together.

So last step, just put 1 and 19 each in a bracket of (x+), since they add up to 20. (If they subtract to reach the number instead, just put the subtracting one as negative)

So, your final answer is (x+1) (x+19).

Note that this method only works for if the coefficient of x^2 is 1, (which is not written out as multiplied by 1 is still the same number).