For each term in this expression, we will notice that each shares a variable of . This can be pulled out as a common factor.

There are no more common factors, and this is the reduced form.

The answer is:

First, factor the numerator, which should be . Now the left side of your equation looks like

Second, cancel the "like" terms - - which leaves us with .

Third, solve for by setting the left-over factor equal to 0, which leaves you with

Let's split the four terms into two groups, and find the GCF of each group.

First group:

Second group:

The GCF of the first group is . When we divide the first group's terms by , we get: .

The GCF of the second group is . When we divide the second group's terms by , we get: .

We can rewrite the original expression,

as,

The common factor for BOTH of these terms is .

Dividing both sides by gives us:

Because the term has a coefficient, you begin by multiplying the and the terms () together: .

Find the factors of that when added together equal the second coefficient (the term) of the polynomial: .

There are four factors of : , and only two of those factors, , can be manipulated to equal when added together and manipulated to equal when multiplied together:

Separate the four terms into two groups, and then find the GCF of each group.

First group:

Second group:

The GCF of the first group is . Factoring out from the terms in the first group gives us:

The GCF of the second group is . Factoring out from the terms in the second group gives us:

We can rewrite the original expression,

as,

We can factor this as:

First, factor the numerator, which should be . Now the left side of your equation looks like

Second, cancel the "like" terms - - which leaves us with .

Third, solve for by setting the left-over factor equal to 0, which leaves you with

For each term in this expression, we will notice that each shares a variable of . This can be pulled out as a common factor.

There are no more common factors, and this is the reduced form.

The answer is:

To find the greatest common factor of a polynomial expression, we need to find all of the factors each term has in common. The easiest way to do this is to first look at the "coefficients", the "real numbers" to the left of the variable.

The first term has "20," the second term has "30," and the third term has "10."

The biggest common factor of these three numbers is "10".

Next, we look at the variable, x.

The first term has x^3, or three x's, the second term has x, or one x, and the third has x^2, or two x's.

The biggest common factor is "x", because while the first and third terms have more x's, the second term only has one x, so we can't pull out any more.

The greatest common factor is 10x, and when you divide each of the three terms by 10x, you get:

We are going to use factoring by grouping to factor this expression.

The expression:

has the form:

In factoring by grouping, we want to split that B value into two smaller values a and b so we end up with this expression:

The rules are:

and

For our problem A=6 B=-13 C=6

So we have:

Another way of saying this is that we are looking for factors of 36 that add up to -13

The values that work are:

Plugging those values in:

Now let's group and factor out from both groups:

Finally let's factor out a (2x-3) from both terms: and we get our answer:

To find the greatest common factor of a polynomial expression, we need to find all of the factors each term has in common. The easiest way to do this is to first look at the "coefficients", the "real numbers" to the left of the variable.

The first term has "20," the second term has "30," and the third term has "10."

The biggest common factor of these three numbers is "10".

Next, we look at the variable, x.

The first term has x^3, or three x's, the second term has x, or one x, and the third has x^2, or two x's.

The biggest common factor is "x", because while the first and third terms have more x's, the second term only has one x, so we can't pull out any more.

The greatest common factor is 10x, and when you divide each of the three terms by 10x, you get: