Question

| What is the factored form of 2x2 – 200 ?

Answer 1

Explanation:

If your equation is
`2x^2-200` and you're to factor it, the first thing you do is set the expression equal to 0 so you can solve for x.

`2x^2-200=0`

There's a couple of different ways in which to approach this. You can factor out a 2:

`2(x^2-100)=0`

and solve it from there. The Zero Product Property says that if the equation is equal to 0, then either 2 has to equal 0 or
`x^2-100` has to equal 0. We know that 2 does not equal 0, so
`x^2-100=0`

Add 100 to both sides in the equation:

`x^2=100`

and then take the square root of both sides. Because this is a second degree polynomial, we expect to have 2 solutions, and we do. Don't forget that when you take the square root of a number you have to alow for both the positive and the negative of the result. Our factored form of the given equation then is that x = 10 and x = -10.

Answer 2

2(x - 10)(x + 10)

Explanation:

Given

2x² - 200 ← factor out 2 from each term

= 2(x² - 100) ← x² - 100 is a difference of squares and factors as

x² - 100 = x² - 10² = (x - 10)(x + 10), hence

2x² - 200 = 2(x - 10)(x + 10)