Factor 2x2−8x−10 completely.

Step 1
Given,
${\displaystyle 2x^2-8x-10}$
To split the middle term:
Multiplying the coefficient of ${\displaystyle x^2}$ and the constant term ${\displaystyle =-20}$
The coefficient of ${\displaystyle =-8}$
We want the product of two numbers to be -20 and sum of the same two numbers to be -8
Cleartly, the numbers are -10 and 2
Step 2
Therefore, we split the middle term accordingly, we have
${\displaystyle 2x^2-8x-10}$
${\displaystyle =2x^2-10+2x-10}$
Taking 2x common from ${\displaystyle 1^{st}}$ two terms and 2 common from last two terms, we have
${\displaystyle =2x(x-5)+2(x-5)}$
Again, taking ${\displaystyle x-5}$ common from the complete expression, we have
${\displaystyle =(x-5)(2x+2)}$
${\displaystyle =2(x+1)(x-5)}$
Therefore, ${\displaystyle 2x^2-8x-10=2(x+1)(x-5)}$