Factor 2x^2 - 3x - 20.

Step-by-step solution

1. 1

   Multiply $a$ by $c$.

   $ac=2\cdot(-20)=-40$

   We want two integers with product $-40$ and sum $-3$.

2. 2

   Search the factor pairs of $40$ with opposite signs. $(1,-40),(2,-20),(4,-10),(5,-8),(8,-5),(10,-4)$ give sums $-39,-18,-6,-3,3,6$. The pair is $5$ and $-8$.

3. 3

   Split the middle term and group in the order that works.

   $2x^2+5x-8x-20=x(2x+5)-4(2x+5)$

   Here the grouping pairs the first two and last two terms; the common binomial $(2x+5)$ emerging from both is the confirmation.

4. 4

   Factor out the shared binomial.

   $2x^2-3x-20=(2x+5)(x-4)$

5. 5

   Verify. $(2x+5)(x-4)=2x^2-8x+5x-20=2x^2-3x-20$ $\checkmark$. At $x=1$: original $=2-3-20=-21$, and $(7)(-3)=-21$ $\checkmark$.