Factoring x2+4 and Special Cubed Theorems: Homework Help

[hockeyfghts5]

Homework Statement

can u factor x²+4
and can't seem to remember the the difference of cubes and isn't there another special cubed theorem.

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

Homework Statement

can u factor x²+4
and can't seem to remember the the difference of cubes and isn't there another special cubed theorem.

It can be factored but it won't be factored with real numbers. You'd need to introduce the imaginary constant,i, such that i²=-1 and use that to factor.

 

[Mark44]

x² + 4 = (x + 2i)(x - 2i), where i is the imaginary unit rock.freak667 mentioned.
Here are the sum and difference of cubes formulas:
x³ + a³ = (x + a)(x² - ax + a²)
x³ - a³ = (x - a)(x² + ax + a²)

 

[hockeyfghts5]

thanks, so i have another question if someone can help me.

lim x³-6²+11x-6
x->-1 x³-4x²-19x +14
i can't seem how to factor the top out if i even need to do that or the bottom

 

[rock.freak667]

thanks, so i have another question if someone can help me.

lim x³-6²+11x-6
x->-1 x³-4x²-19x +14
i can't seem how to factor the top out if i even need to do that or the bottom

Why would you need to factor it? Did you evaluate it at x=-1? Was it in the indeterminate form 0/0?

 

[Fermat]

If the numerator, or denominator, goes to zero when x = 1, then (x-1) is a factor.

You can factor it out by dividing (x-1) into the numerator, say, in the style of long-division.