Polynomials - Algebra

First, set up the division as the following:

Look at the leading term in the divisor and in the dividend. Divide by gives ; therefore, put on the top:

Then take that and multiply it by the divisor, , to get . Place that under the division sign:

Subtract the dividend by that same and place the result at the bottom. The new result is , which is the new dividend.

Now, is the new leading term of the dividend. Dividing by gives 5. Therefore, put 5 on top:

Multiply that 5 by the divisor and place the result, , at the bottom:

Perform the usual subtraction:

Therefore the answer is with a remainder of , or .

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To find the degree of a polynomial, simply find the highest exponent in the expression. As two is the highest exponent above, it is also the degree of the polynomial.

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

Simplify the following expression:

Let's begin by putting each polynomial in standard form (decreasing exponent order)

Good, see how the highest exponents are on the left, and the lowest are on the right? That's standard form.

Next, let's remove the parentheses and put terms with the same exponent next to eachother.

Okay, finally, combine like terms by adding the coefficients (the numbers out front).

Notice that the squared terms cancel out, and the fifth term stays the same.

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

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:

Adding polynomials is very simple. It's just a matter of collecting like terms. This means that we look to see if there are similar terms that can have their coefficients added. When we can no longer do this, we have reached our final answer.

Distributing the plus sign to every term in the polynomial right of the sign, we can omit the parentheses.

Now we are left to collect like terms until we've reached our final answer.

Adding polynomials is very simple. It's just a matter of collecting like terms. This means that we look to see if there are similar terms that can have their coefficients added. When we can no longer do this, we have reached our final answer.

Distributing the plus sign to every term in the polynomial right of the sign, we can omit the parentheses.

Now we are left to collect like terms until we've reached our final answer.

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):

To find the degree of a polynomial, simply find the highest exponent in the expression. As two is the highest exponent above, it is also the degree of the polynomial.

We must begin by combining like terms. Remember that like terms are those that contain the same variables, raised to the same power. This leads us to the following operations:

When we add and subtract accordingly, we are left with:

. Remember, do not add the exponents in this case--only when the terms are being multiplied.

We are asked to expand and simplify the expression: .

This question is going to require knowledge of exponent rules and FOIL methods.

The first step is to create an inverse reciprocal of a negative exponent.

Now, we can expand the expression by removing the exponent in the denominator.

Use the FOIL method to first multiply and .

You'll find it creates . Replace it back into the expression because we have to multiply the result by one more time.

Be careful with exponents and coefficients!

Combine like terms to find the simplified answer.

To find the degree of a polynomial, simply find the highest exponent in the expression. As five is the highest exponent above, it is also the degree of the polynomial.