Question

How do you factor the equation y = -2x^2 +3x +5 into the form y = (x-p)(x-q)?

Answer 1

`y=(x+1)(-2x+5)`

Explanation:

`y=-2x^2 +3x +5`

you need to factor this by grouping:

`y=ax^2 + bx +c`

we need to find factors of `a*c` that add up to `b`:

`a*c=-2*5` and `-2+5 = 3` so let's split the parts, we split the `bx` term into `h+k=b`

`y=-2x+5x = 3x`

Now replace the `3x` in our quadratic equation:

`y=-2x^2 -2x+5x +5`

now group:

`y=(-2x^2 -2x)+(5x +5)`

use the distributive property:

`y=-2x(x +1)+5(x +1)`

factor out `(x+1)`

`y=(x+1)(-2x+5)`

Answer 2

`(-2x+5)(x+1)`

Explanation:

We can start by factoring by grouping. Here, we'll split up the `b` term into two terms so we can factor them separately.

We can rewrite `3x` as `-2x` and `5x`. Thus, we have

`color(blue)(-2x^2-2x)+color(purple)(5x+5)`

We can factor out a `-2` out of the blue term and a `5` out of the purple term. Doing this, we get

`-2x(x+1)+5(x+1)`

Both terms have an `(x+1)` in common, so we can factor that out. We get

`(-2x+5)(x+1)`

as our final answer.

Hope this helps!