Question
Factor the expression x^2 + 11x + 28
Answers
Answered by
GPT-4o mini
To factor the quadratic expression \(x^2 + 11x + 28\), we need to find two numbers that multiply to 28 (the constant term) and add up to 11 (the coefficient of the linear term).
The pairs of factors of 28 are:
- \(1 \times 28\)
- \(2 \times 14\)
- \(4 \times 7\)
Among these pairs, \(4\) and \(7\) add up to \(11\):
\[
4 + 7 = 11
\]
Thus, we can factor the expression as:
\[
x^2 + 11x + 28 = (x + 4)(x + 7)
\]
So, the factored form of the expression \(x^2 + 11x + 28\) is:
\[
\boxed{(x + 4)(x + 7)}
\]
The pairs of factors of 28 are:
- \(1 \times 28\)
- \(2 \times 14\)
- \(4 \times 7\)
Among these pairs, \(4\) and \(7\) add up to \(11\):
\[
4 + 7 = 11
\]
Thus, we can factor the expression as:
\[
x^2 + 11x + 28 = (x + 4)(x + 7)
\]
So, the factored form of the expression \(x^2 + 11x + 28\) is:
\[
\boxed{(x + 4)(x + 7)}
\]