M2 + 8m + 7

m² + 5m + 6

m2 + 10m + 9

m2 - 6m + 8

m2 - 8m + 12

m2 + 11m + 24

How do I factor each trinomial?

m² + 8m + 7 = (m + 1) (m + 7)

m² - 6m + 8 = (m - 2) (m - 4)

Step-by-step explanation:

If a trinomial ax² + bx + c is "factorable", you can use the AC method.

1. Multiply a and c.

2. Find factors of ac that add up to b.

3. Divide the factors by a and reduce.

4. The numerators are the constants, the denominators are the coefficients.

For example:

m² + 8m + 7

a = 1, b = 8, c = 7

1. ac = 1*7 = 7

2. Factors of 7 that add up to 8 are 1 and 7.

3. Divide by 1: 1/1 and 7/1

4. The factors are (m + 1) and (m + 7).

Therefore, m² + 8m + 7 = (m + 1) (m + 7).

Let's try one with a negative coefficient:

m² - 6m + 8

a = 1, b = - 6, c = 8

1. ac = 1*8 = 8

2. Factors of 8 that add up to - 6 are - 2 and - 4.

3. Divide by 1: - 2/1 and - 4/1

4. The factors are (m - 2) and (m - 4)

Therefore, m² - 6m + 8 = (m - 2) (m - 4).

You can check your answers by distributing.