This polynomial is formed by multiplying two factors that look something like this:

In order to successfully factor a polynomial, find the factors of 12 that add up to 7.

They are 3 and 4.

That gives you the answer .

This polynomial is formed by multiplying two factors that look something like this:

In order to successfully factor a polynomial, find the factors of 6 and factors of 3 that, when combined, add up to -11.

They are 3 and 2 and -1 and -3.

That gives you the answer .

Factoring a polynomial is the reverse of distributing. What common factor exists for both  and ? We know that 

and

So we can factor out  from the expression and get 

Don't forget the negative sign!

First, since there are no subtractive operations in the original expression, start by noting that all signs within the factors will be positive (i.e. (x + x)(x + x)).

Then, look at the highest degree variables.

We have .

The only possible ways to factor that are

 and .

Then look at .

The only way to fact that is , so we know that 2x and x will appear in our final answer.

Write down .

Then, try inserting the possibilities we came up with for creating  into the blank spaces.

By trying the various permutations you should come up with the answer.

The goal is to get x by itself on one side.

Start by getting all terms with x in them on the left side of the equation.

Add  to each side to get

.

Then, factor x out of the left side of the equation to get

.

Divide each side of the equation by  to solve for x and get the answer to the problem.

Remember to read the question carefully.

It asks you to solve for h, not x.

So you can eliminate two answers right away.

Then, look to see if you can factor anything.

Factor x out of the right side of the equation to get

.

Divide both sides of the equation by x to get

.

Then, subtract  from each side and divide by  to get the answer!

Start with the highest exponent. In two factors,  can only be made by multplying  and . Because everything in the original expression is positive, you know that all the factors in the answer also have to be positive.

Write down what you know if the form

.

Now, look at the term with the lowest exponent, 4. You can only make this with positive number by squaring 2 or multiplying 4 by 1. Then notice that the  term is multiplied by 4 and not 2. This means that 4 must be factored into 1 and 4 in our answer. Ths also means that the 4 must be in the factor with , because if it was in the factor with  they would never be multiplied together to create .

Try inserting 1 and 4 into the blank spaces of our previous expression. Foil the expression you created to check your answer.

This may look complicated at first, but it's just a special case of a polynomial called a 'difference of squares.' That means that there are two terms, one is negative, and they are both perfect squares. In this case, the negative is -16. The was to factor this type of polynomial is to follow this formula:

(square root of the positive perfect square + square root of the negative perfect square) x (square root of the positive perfect square - square root of the negative perfect square).

This gives the answer  for this problem.

Remember, you can always check your work by foiling the factored expression out to make sure it matches the original polynomial.

First isolate all terms with x to one side and keep all other terms on the other side.

To this end, multiple both sides of the equation by c.

This gives

.

Then factor x out of the right side of the equation to get

.

Finally, divide both sides of the equation by  to get the answer.

The common factor in this problem is only , because each number in this term share the same factor.  

By pulling this term out of the expression, we need to find , , and  that would match the terms of the problem.

Determine .  Divide by  on both sides.

Determine .

Determine .

Resubstitute the variables.

This means that .

The answer is: