Question

question 21 of 25
which of the binomials below is a factor of this trinomial?
$6x^2 - 7x - 5$

a. $x - 1$
b. $x + 1$
c. $2x - 1$
d. $2x + 1$

Explanation:

Step1: Factor the trinomial

We use the AC method to factor \(6x^{2}-7x - 5\). For a quadratic \(ax^{2}+bx + c\), we find two numbers that multiply to \(a\times c=6\times(- 5)=-30\) and add up to \(b=-7\). The numbers are \(-10\) and \(3\) since \(-10\times3=-30\) and \(-10 + 3=-7\).
Rewrite the middle term: \(6x^{2}+3x-10x - 5\)
Group the terms: \((6x^{2}+3x)-(10x + 5)\)
Factor out the GCF from each group: \(3x(2x + 1)-5(2x + 1)\)
Factor out the common binomial factor \((2x + 1)\): \((3x - 5)(2x+1)\)

Step2: Identify the factor

From the factored form \((3x - 5)(2x + 1)\), we can see that \(2x + 1\) is a factor.

Answer:

D. \(2x + 1\)