What is the factor of this trinomial x2 plus 13x plus 42?

The easiest way to factor x2 + 13x + 42 is to look at the last number.

The last number is 42.

Now, think of what whole numbers you can multiply to equal 42.

1 x 42

2 x 21

3 x 14

6 x 7

If you look at the equation, we notice that the sign pattern is + + +

When the sign pattern is + + +, we know that whatever two factors you choose must add up to the middle number, 13.

So, automatically we can get rid of some of these factors.

1 x 42 --> 1 + 42 doesn't equal 13

2 x 21 --> 2 + 21 doesn't equal 13

3 x 14 --> 3 + 14 doesn't equal 13

Now, we're automatically left with 6 x 7.

So, your answer would be (factored out),

(x+6)(x+7)

Where x = -7, -6