Question

question 3 of 10
which of the binomials below is a factor of this trinomial?
4x² - 4x - 120

a. x + 4
b. x - 6
c. x + 6
d. x - 4

Explanation:

Step1: Factor out the GCF

The trinomial is \(4x^2 - 4x - 120\). First, factor out the greatest common factor (GCF) of 4:
\(4(x^2 - x - 30)\)

Step2: Factor the quadratic

Now factor \(x^2 - x - 30\). We need two numbers that multiply to \(-30\) and add to \(-1\). These numbers are \(-6\) and \(5\), since \(-6 \times 5 = -30\) and \(-6 + 5 = -1\).
So, \(x^2 - x - 30 = (x - 6)(x + 5)\)

Step3: Combine factors

Putting it all together, the factored form of the trinomial is:
\(4(x - 6)(x + 5)\)

Step4: Identify the binomial factor

From the factored form, the binomial factors are \(x - 6\), \(x + 5\), and the GCF 4 (but 4 is not a binomial here). Among the options, \(x - 6\) (Option B) is a factor.

Answer:

B. \(x - 6\)