Intermediate Single-Variable Algebra - 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 .

Use the FOIL method (First, Outer, Inner, Last):

Put all of these terms together:

Combine like terms:

Use the quadratic formula to solve:

To factor and solve for in the equation

Factor out of the equation

Use the "difference of squares" technique to factor the parenthetical term, which provides the completely factored equation:

Any value that causes any one of the three terms , , and to be will be a solution to the equation, therefore

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:

Put the negative exponent on the bottom so that you have which simplifies further to .

First, multiply out the second expression so that you get .

Then, multiply your like terms, taking care to remember that when multiplying terms that have the same base, you add the exponents. Thus, you get .