Questions: Completely factor this trinomial, if possible. x² - 6x - 16

Solution Steps

To factor the trinomial \( x^2 - 6x - 16 \), we need to find two numbers that multiply to the constant term (-16) and add up to the coefficient of the linear term (-6). Once we find these numbers, we can rewrite the trinomial and factor by grouping.

We start with the trinomial: \[ x^2 - 6x - 16 \]

We need to find two numbers, \( a \) and \( b \), such that: \[ a \cdot b = -16 \] \[ a + b = -6 \]

By inspection or trial and error, we find that: \[ a = -8 \] \[ b = 2 \]

We can rewrite the trinomial using the numbers found: \[ x^2 - 6x - 16 = x^2 - 8x + 2x - 16 \]

Group the terms and factor each group: \[ x^2 - 8x + 2x - 16 = x(x - 8) + 2(x - 8) \]

Factor out the common binomial factor: \[ x(x - 8) + 2(x - 8) = (x - 8)(x + 2) \]

Final Answer