Question

1. factor the trinomial: $2x^2 - 5x + 3$

$(x-2)(x-3)$
$(x+1)(2x-3)$
$(3x-2)(x-1)$
$(x-1)(2x-3)$

Explanation:

Step1: Split the middle term

Find two numbers that multiply to $2\times3=6$ and add to $-5$. These numbers are $-2$ and $-3$. Rewrite the trinomial:
$2x^2 -2x -3x +3$

Step2: Group and factor pairs

Group the first two and last two terms, then factor out the GCF from each group:
$2x(x-1) -3(x-1)$

Step3: Factor out common binomial

Factor out $(x-1)$ from both terms:
$(x-1)(2x-3)$

Step4: Verify options

Compare the result to the given choices.

Answer:

D. $(x-1)(2x-3)$