Question

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

Answer 1

Answer:

2(x - 10)(x + 10)

Step-by-step 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)

Answer 2

Answer:

Step-by-step 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.