To factor the quadratic expression \(x^2 + 20x + 99\), we need to find two numbers that multiply to \(99\) (the constant term) and add up to \(20\) (the coefficient of the linear term). The factors of \(99\) that we can consider are: - \(1 \times 99\) - \(3 \times 33\) - \(9 \times 11\) Now we check which pair adds up to \(20\): - \(1 + 99 = 100\) - \(3 + 33 = 36\) - \(9 + 11 = 20\) The pair \(9\) and \(11\) multiplies to \(99\) and adds up to \(20\). Thus, we can factor the quadratic as: \[ x^2 + 20x + 99 = (x + 9)(x + 11) \] So, the factored form of the expression is \( (x + 9)(x + 11) \).

factor x^2+20x+99

1 answer

To factor the quadratic expression \(x^2 + 20x + 99\), we need to find two numbers that multiply to \(99\) (the constant term) and add up to \(20\) (the coefficient of the linear term).

The factors of \(99\) that we can consider are:

\(1 \times 99\)
\(3 \times 33\)
\(9 \times 11\)

Now we check which pair adds up to \(20\):

\(1 + 99 = 100\)
\(3 + 33 = 36\)
\(9 + 11 = 20\)

The pair \(9\) and \(11\) multiplies to \(99\) and adds up to \(20\).

Thus, we can factor the quadratic as:

\[ x^2 + 20x + 99 = (x + 9)(x + 11) \]

So, the factored form of the expression is \( (x + 9)(x + 11) \).