Question

X^2-11x+24
I need to convert the quadratic equation from expanded to factored form

Answer 1

`(x - 3) \: (x - 8)`

Explanation:

We were given the equation:

`{x}^(2) - 11x + 24 = 0`

Therefore in order to factorize we first need to find the numbers that add to be equal to -11 and multiply to be equal to 24. The two numbers are:

`- 8 \: and \: - 3 \\ \\ - 8 + ( - 3) = - 11 \\ - 8 * - 3 = 24`

So the new equation is

`{x}^(2) - 8x - 3x + 24 = 0 \\ \\ factorize: ( {x}^(2) - 8x) \: ( - 3x + 24) = 0 \\ \\ x(x - 8) \: - 3(x - 8) \\ \\ therefore : (x - 3) \: ( x - 8) = 0`

Answer 2

Explanation:

Comment

There are a lot of choices. Luckily the middle term is minus and the third term is plus, so you don't have to juggle minus signs around. Both factors are minus when put together with x.

-3 - 8

-4 - 6

-2 -12

-1 - 14

I think these are all the possible factors.

-4 + - 6 = - 10 Not the answer. It needs to be - 11

-2 + -12 = -14 Not the answer. It needs to be - 11

-1 + - 24 = -25 Just about as far away as you can get. Not the answer

So A must be right

-3 + -8 = - 11

That's what it should be. So the factors are

Answer:

(x -3)(x - 8)= x^2 - 11x + 24