Question

1. factor. $3x^{2}-10x-8$

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Explanation:

Step1: Find product of leading & constant term

$3 \times (-8) = -24$

Step2: Identify pair summing to middle term

Find two numbers that multiply to $-24$ and add to $-10$: $-12$ and $2$.

Step3: Split middle term

$3x^2 - 12x + 2x - 8$

Step4: Factor by grouping

$$\begin{align} &3x(x - 4) + 2(x - 4) \\ &=(3x + 2)(x - 4) \end{align}$$

Answer:

$(3x + 2)(x - 4)$