Question
Factor the given polynomial.
x squared plus 8 x plus 15
x squared plus 8 x plus 15
Answers
GPT-4o mini
To factor the polynomial \( x^2 + 8x + 15 \), we need to find two numbers that multiply to 15 (the constant term) and add up to 8 (the coefficient of the linear term).
The numbers that satisfy these conditions are 3 and 5, since:
- \( 3 \times 5 = 15 \)
- \( 3 + 5 = 8 \)
Thus, we can factor the polynomial as follows:
\[
x^2 + 8x + 15 = (x + 3)(x + 5)
\]
Therefore, the factored form of the polynomial is:
\[
(x + 3)(x + 5)
\]
The numbers that satisfy these conditions are 3 and 5, since:
- \( 3 \times 5 = 15 \)
- \( 3 + 5 = 8 \)
Thus, we can factor the polynomial as follows:
\[
x^2 + 8x + 15 = (x + 3)(x + 5)
\]
Therefore, the factored form of the polynomial is:
\[
(x + 3)(x + 5)
\]