Question

9.) $2x^2+9x-35$

Explanation:

Step1: Find product of a and c

For $ax^2+bx+c$, $a=2$, $c=-35$.
$\text{Product} = 2\times(-35) = -70$

Step2: Find pair summing to b=9

Find two numbers that multiply to -70 and add to 9: 14 and -5.
$14\times(-5) = -70$, $14+(-5)=9$

Step3: Split middle term

Rewrite $9x$ as $14x-5x$:
$2x^2 + 14x - 5x - 35$

Step4: Factor by grouping

Group terms and factor out GCFs:
$2x(x+7) - 5(x+7)$
Factor out $(x+7)$:
$(2x-5)(x+7)$

Answer:

$(2x-5)(x+7)$