Question

How do you factor `21 - 4x - x^2`?

Answer 1

The factored quadratic is `-(x-3)(x+7)`.

Explanation:

First, factor out a `-1` so that the `x^2` term is positive (and also first):

`color(white)=21-4x-x^2`

`=-(-21+4x+x^2)`

`=-(x^2+4x-21)`

Now, we have to find two numbers that multiply to `-21` and add up to `4`. These numbers are `7` and `-3`. Split up the `x` term into these numbers, then factor them separately and combine later:

`=-(x^2+7x-3x-21)`

`=-(color(red)x(x+7)-3x-21)`

`=-(color(red)x(x+7)-color(blue)3(x+7))`

`=-((color(red)x-color(blue)3)(x+7))`

`=-(color(red)x-color(blue)3)(x+7)`

That's the factored quadratic. Hope this helped!

Answer 2

-(x - 3)(x + 7)

Explanation:

`y = -x^2 - 4x + 21`
`y = - (x^2 + 4x - 21)`
Find 2 numbers knowing the sum (b = 4) and the product (c = -21).
They are -3 and 7.
Factored form:
`y = - (x - 3)(x + 7)`