Factor.

x, squared, plus, 8, x, plus, 7
x
2
+8x+7

1 answer

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:

\[ (x + 1)(x + 7) \]