Question

1. $6x^2 + 7x - 20$
2. $2x^2 - 5x + 3$

Explanation:

Step1: Factor $6x^2+7x-20$

Find two numbers: product $6\times(-20)=-120$, sum $7$. The numbers are $15$ and $-8$.
Rewrite and factor:

$$\begin{align*} 6x^2+15x-8x-20&=3x(2x+5)-4(2x+5)\\ &=(3x-4)(2x+5) \end{align*}$$

Step2: Factor $2x^2-5x+3$

Find two numbers: product $2\times3=6$, sum $-5$. The numbers are $-2$ and $-3$.
Rewrite and factor:

$$\begin{align*} 2x^2-2x-3x+3&=2x(x-1)-3(x-1)\\ &=(2x-3)(x-1) \end{align*}$$

Answer:

1. $6x^2+7x-20=(3x-4)(2x+5)$
2. $2x^2-5x+3=(2x-3)(x-1)$