Question

1. $3x^{2}-x-10$

Explanation:

Step1: Identify coefficients

For $3x^2 - x - 10$, $a=3$, $b=-1$, $c=-10$

Step2: Find factor pair

Find two numbers: product $a \cdot c = 3 \times (-10) = -30$, sum $b=-1$. The numbers are $5$ and $-6$.

Step3: Split middle term

Rewrite the quadratic:
$3x^2 + 5x - 6x - 10$

Step4: Group and factor

Group terms and factor out GCF:
$x(3x + 5) - 2(3x + 5)$

Step5: Factor out common binomial

Factor out $(3x + 5)$:
$(3x + 5)(x - 2)$

Answer:

$(3x + 5)(x - 2)$