Can x^2+0x-2 be factored?

Question

Can this equation be factored? And if so, would you use the diamond method?

Also, if possible, what are the factors for this equation?

Thanks!

Answer 1

Hello, Maddie!

 

I'm not familiar with the diamond method, but x² + 0x - 2 can be factored, and let's see why.

This is a polynomial in the form of ax² + bx + c.

 

If we look at polynomial, we can see that c = -2.  Because c is negative, we know that our factorization must have the form of:

 

(x + ?)(x - ?)

 

Because... you can only get a negative c if you have one positive and one negative factor.  When you multiple two negatives, for instance, you end up with a positive.  So you need one positive and one negative.

 

Because b = 0, we need to find two numbers that will add up to 0, but also multiple and equal to 2.

 

y - z = 0

y*z = 2

 

So then we solve the system.

 

y = z

(z)(z) = 2

 

z² = 2

 

z = sqrt(2)

 

So, the factor of this polynomial is:

 

(x + √(2))(x - √(2))

 

Answer 2

x² - 2 can be factored over the set of irrationals:

 

(x + √2)(x - √2)

 

You do not give an equation. Equations are not factored. Polynomials are factored.