# How do you factor 2x^2+3x-20?

Nov 9, 2015

#### Answer:

$\left(x + 4\right) \left(2 x - 5\right)$

#### Explanation:

The left and right side of the polynomial:
$5 \times \left(4\right)$$= 20$
$2 \times \left(- 1\right)$$= 2$

How can multiply those together and add to $3$?
$5 \times - 1$ = $- 5$
and
$2 \times 4$ = $8$
If we add $- 5 + 8$, we get $3$!!!

Because we need $1 x \cdot \left(- 5\right) = - 5 x$
and
$2 x \cdot 4 = 8 x$
We put each term across from each other.
So its like cross multiplying

$\left(1 x + 4\right)$
$\left(2 x - 5\right)$

Try if you get the middle term of $3 x$
$\left(1 x \cdot - 5\right) + \left(2 x \cdot 4\right) = 3 x$

Now the answer can be written as $\left(x + 4\right) \left(2 x - 5\right)$