Question

factor trinomials (a=1)
score: 3/5 penalty: 1 off
question
factor.
$x^2 - 4x - 21$
answer

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-21\) (the constant term) and add up to \(-4\) (the coefficient of \(x\)). Let's list the factor pairs of \(-21\): \((-7, 3)\) because \(-7\times3 = -21\) and \(-7 + 3=-4\).

Step2: Factor the trinomial

Using the numbers we found, we can factor the quadratic \(x^{2}-4x - 21\) as \((x - 7)(x + 3)\) since when we expand \((x - 7)(x + 3)\), we get \(x^{2}+3x-7x - 21=x^{2}-4x - 21\).

Answer:

\((x - 7)(x + 3)\)