Question
Factor this polynomial
x^2 + 7x + 12
x^2 + 7x + 12
Answers
GPT-4o mini
To factor the polynomial \( x^2 + 7x + 12 \), we need to find two numbers that multiply to the constant term (12) and add up to the linear coefficient (7).
The pairs of factors of 12 are:
- 1 and 12 (1 + 12 = 13)
- 2 and 6 (2 + 6 = 8)
- 3 and 4 (3 + 4 = 7)
The pair that adds up to 7 is 3 and 4.
Thus, we can factor the polynomial as follows:
\[
x^2 + 7x + 12 = (x + 3)(x + 4)
\]
So the factored form is:
\[
(x + 3)(x + 4)
\]
The pairs of factors of 12 are:
- 1 and 12 (1 + 12 = 13)
- 2 and 6 (2 + 6 = 8)
- 3 and 4 (3 + 4 = 7)
The pair that adds up to 7 is 3 and 4.
Thus, we can factor the polynomial as follows:
\[
x^2 + 7x + 12 = (x + 3)(x + 4)
\]
So the factored form is:
\[
(x + 3)(x + 4)
\]