Question

Factor each trinomial completely. If a polynomial can't be factored, write "prime." See Examples 1 through 8. 1. x^2 + 7x + 6

Answer 1

Answer:

(x + 1) (x + 6)

Step-by-step explanation:

Factoring a polynomial means to "break" a polynomial into a product of other smaller polynomials.

When you have a trinomial you can look for common factors, if you don't have any common factors then you can proceed with other options.

The trinomial we have is: x² + 7x + 6 and it doesn't have any common factors.

• To factor this trinomial we are going to "break" the x² into x and x

x

x

• Then, we need to find two numbers whose sum is 7 (linear term of the trinomial)  and the result of their multiplication is 6 (independent term of the trinomial).

The numbers 6 and 1 can do: 6 x 1 = 6 and 6 + 1 = 7

• Now we are going to pair each one of these numbers with our x's from the first step and we get

(x + 1) (x + 6)

Therefore, the factorization of x² + 7x + 6 = (x + 1) (x + 6)