Question

factor the trinomial, or state that the trinomial is prime.
$2x^2 - 5x - 3$
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. $2x^2 - 5x - 3 = \square$ (factor completely.)
b. the polynomial is prime.

Explanation:

Step1: Use AC method for factoring

For trinomial \(ax^2 + bx + c\) (here \(a = 2\), \(b=-5\), \(c = - 3\)), find two numbers that multiply to \(a\times c=2\times(-3)=-6\) and add up to \(b=-5\). The numbers are \(-6\) and \(1\) since \(-6\times1=-6\) and \(-6 + 1=-5\).

Step2: Rewrite the middle term

Rewrite \(-5x\) as \(-6x+x\), so the trinomial becomes \(2x^{2}-6x + x-3\).

Step3: Group and factor

Group the first two terms and the last two terms: \((2x^{2}-6x)+(x - 3)\). Factor out the GCF from each group: \(2x(x - 3)+1(x - 3)\). Then factor out \((x - 3)\) to get \((2x + 1)(x - 3)\).

Answer:

A. \(2x^{2}-5x - 3=(2x + 1)(x - 3)\)