Answer:
(x + 1) (x + 6)
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)