Factoring Polynomials - Math

You can see that each term in the equation has an "x", therefore by factoring "x" from each term you can get that the equation equals .

This is a difference of perfect cubes so it factors to . Only the first expression will yield an answer when set equal to 0, which is 1. The second expression will never cross the -axis. Therefore, your answer is only 1.

Factor the equation to . Set and get one of your 's to be . Then factor the second expression to . Set them equal to zero and you get .

Use the difference of perfect cubes equation:

In ,

and

First consider all the factors of 12:

1 and 12

2 and 6

3 and 4

Then consider which of these pairs adds up to 7. This pair is 3 and 4.

Therefore the answer is .

Begin by extracting from the polynomial:

Now, factor the remainder of the polynomial as a difference of cubes:

Begin by rearranging like terms:

Now, factor out like terms:

Rearrange the polynomial:

Begin by rearranging like terms:

Now, factor out like terms:

Rearrange the polynomial:

Factor:

Begin by separating into like terms. You do this by multiplying and , then finding factors which sum to

Now, extract like terms:

Simplify:

To begin, distribute the squares:

Now, combine like terms:

Begin by extracting from the polynomial:

Now, distribute the cubic polynomial:

Begin by extracting like terms:

Now, rearrange the right side of the polynomial by reversing the signs:

Combine like terms:

Factor the square and cubic polynomial:

Begin by rearranging the terms to group together the quadratic:

Now, convert the quadratic into a square:

Finally, distribute the :

Begin by extracting from the polynomial:

Now, rearrange to combine like terms:

Extract the like terms and factor the cubic:

Simplify by combining like terms:

Begin by extracting from the polynomial:

Now, rearrange to combine like terms:

Extract the like terms and factor the cubic:

Simplify by combining like terms:

The product of the last two numbers should be 6, while the sum of the products of the inner and outer numbers should be 5x. Factors of six include 1 and 6, and 2 and 3. In this case, our sum is five so the correct choices are 2 and 3. Then, our factored expression is (x + 2)(x + 3). You can check your answer by using FOIL.

y = x2 + 5x + 6

2 * 3 = 6 and 2 + 3 = 5

(x + 2)(x + 3) = x2 + 5x + 6

LCM of

LCM of

and since

The LCM

When working with a rational expression, you want to first put your monomials in standard format.

Re-order the bottom expression, so it is now reads .

Then factor a out of the expression, giving you .

The new fraction is .

Divide out the like term, , leaving , or .

The polynomial factors into (x + 3) (3x - 2).

3x² + 7x – 6 = (a + b)(c + d)

There must be a 3x term to get a 3x² term.

3x² + 7x – 6 = (3x + b)(x + d)

The other two numbers must multiply to –6 and add to +7 when one is multiplied by 3.

b * d = –6 and 3d + b = 7

b = –2 and d = 3

3x² + 7x – 6 = (3x – 2)(x + 3)

(x + 3) is the correct answer.

This is a difference of squares. The difference of squares formula is _a_2 – _b_2 = (a + b)(a – b).

In this problem, a = 6_x_ and b = 7_y_:

36_x_2 – 49_y_2 = (6_x_ + 7_y_)(6_x_ – 7_y_)