To factor the quadratic expression \( x^2 + 8x + 7 \), we are looking for two numbers that multiply to the constant term (which is 7) and add up to the coefficient of the \( x \) term (which is 8).
The pairs of factors of 7 are:
- \( 1 \) and \( 7 \)
- \( -1 \) and \( -7 \)
The pair \( 1 \) and \( 7 \) add up to \( 8 \).
Therefore, we can factor the expression as follows:
\[ x^2 + 8x + 7 = (x + 1)(x + 7) \]
So, the factored form of \( x^2 + 8x + 7 \) is:
\[ (x + 1)(x + 7) \]
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