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Factoring Polynomials

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Factoring the Difference or Sum of Two Cubes

A. Factor each polynomial completely, given that the binomial following it is a factor of the polynomial.
B. Factor each polynomial completely.
C. Factor each polynomial completely, if prime say so.
D. Factor each polynomial completely, if prime say so.
E. Decreasing cube. Each of the three dimensions of a cube with a volume of [see attachment] cubic centimeters is decreased by a whole number of centimeters. If a new volume is [see attachment] cubic centimeters and the new width is y - 6 centimeters, then what are the new length and height?

Solving Quadratic Equations by Factoring

F. Solve the equation using zero factor property
G. Solve the equation using zero factor property
H. Solve each equation with repeated or three solutions.

Please demonstrate. Please see attached file.

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Factoring is mostly a process of trial and error, then checking your answer by multiplying it out. You won't learn by looking at my answers; you'll only learn if you do all the problems yourself. Once you do that, check your answers against mine.

Factoring the Difference or Sum of Two Cubes

A. Factor each polynomial completely, given that the binomial following it is a factor of the polynomial.

Since we know that x + 3 is a factor, the first step is to divide the polynomial by x + 3:

x2 - x - 2
x + 3 | x3 + 2x2 - 5x - 6
-(x3 + 3x2)
0 - x2 - 5x - 6
-(-x2 - 3x)
0 -2x - 6

So, now we know that x3 + 2x2 - 5x - 6 = (x + 3)(x2 - x - 2). Now, we can try to factor x2 - x - 2.

x2 - x - 2 = (x - 2)(x + 1)

[Verify that this is true by multiplying it out.]

Therefore, the answer is:

x3 + 2x2 - 5x - 6 = (x + 3)(x - 2)(x + 1)

B. Factor each polynomial completely.

u3 = 125v3
125v3 - u3 = ...

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