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: Split middle term

Find two numbers that multiply to $2\times(-3)=-6$ and add to $-5$. These numbers are $-6$ and $1$.
$2x^2 -6x + x -3$

Step2: Group and factor pairs

Group first two and last two terms, factor GCF from each group.
$2x(x - 3) + 1(x - 3)$

Step3: Factor out common binomial

Extract the shared binomial factor.
$(2x + 1)(x - 3)$

Answer:

A. $2x^{2}-5x-3=(2x+1)(x-3)$ (Factor completely.)