Question

2x² + 5x - 18

Explanation:

Step1: Identify coefficients

For $ax^2+bx+c$, $a=2$, $b=5$, $c=-18$

Step2: Find factor pair

Find two numbers: product $a\times c=2\times(-18)=-36$, sum $b=5$. The numbers are 9 and -4.

Step3: Split middle term

Rewrite $5x$ as $9x-4x$:
$2x^2 + 9x - 4x - 18$

Step4: Factor by grouping

Group terms and factor out GCF:
$x(2x+9) - 2(2x+9)$

Step5: Factor common binomial

Extract $(2x+9)$:
$(2x+9)(x-2)$

Answer:

$(2x+9)(x-2)$