Question

question 5 of 10
which of the binomials below is a factor of this trinomial?
$5x^2 + 20x + 15$

a. $x + 1$
b. $x + 5$
c. $x - 1$
d. $x - 5$

Explanation:

Step1: Factor out the GCF

First, factor out the greatest common factor (GCF) from the trinomial \(5x^2 + 20x + 15\). The GCF of 5, 20, and 15 is 5. So we have:
\(5(x^2 + 4x + 3)\)

Step2: Factor the quadratic

Now, factor the quadratic \(x^2 + 4x + 3\). We need two numbers that multiply to 3 and add to 4. Those numbers are 1 and 3. So, \(x^2 + 4x + 3=(x + 1)(x + 3)\).

Step3: Combine the factors

Putting it all together, the factored form of the trinomial is \(5(x + 1)(x + 3)\). So, one of the binomial factors is \(x + 1\).

Answer:

A. \(x + 1\)