Polynomials - Algebra

First distribute the :

Then distribute the :

Finally combine like terms:

Since we are only adding and subtracting (there is no multiplication or division), we can remove the parentheses.

Regroup the expression so that like variables are together. Remember to carry positive and negative signs.

For all fractional terms, find the least common multiple in order to add and subtract the fractions.

Combine like terms and simplify.

With this problem, you need to take the trinomials out of parentheses and combine like terms. Since the two trinomials are being added together, you can remove the parentheses without needing to change any signs:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms:

With this problem, you need to distribute the two fractions across each of the trinomials. To do this, you multiply each term inside the parentheses by the fraction outside of it:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms. Since you have a positive and negative , those two terms will cancel out:

To add these two trinomials, you will first begin by combining like terms. You have two terms with , two terms with , and two terms with no variable. For the two fractions with , you can immediately add because they have common denominators:

To add trinomials, identify and group together the like-terms: . Next, factor out what is common between the like-terms:. Finally, add what is left inside the parentheses to obtain the final answer of .

First, we want to eliminate the variable from the set of equations. To do this, we need to make the coefficients of the two 's equal but opposite. This way, when we add the equations, we will be able to eliminate them. To make the equal but opposite to the , we need to multiply the top equation by 2 on both sides. This gives us the equation:

Then, we combine the two equations by adding them. We add the like terms together and get this equation:

Using our knowledge of algebra, we know we can divide both sides by 7 to isolate the . Doing so leaves us with our answer, .

To solve this problem, simply add the terms with like exponents and variables:

Thus, is our answer.

The first step is to combine all terms with like exponents and variables. Watch for negative signs!

Next, rearrange into standard quadratic form :

Thus, our answer is .

Let's solve this problem the long way, to see how it's done. Then we can look at a shortcut.

First, FOIL the binomial combinations:

FOIL stands for the multiplication between the first terms, outer terms, inner terms, and then the last terms.

Lastly, add the compatible terms in our trinomials:

So, our answer is .

Now, let's look at a potentially faster way.

Look at our initial problem.

Notice how can be found in both terms? Let's factor that out:

Simpify the second term:

Now, perform a much easier multiplication:

So, our answer is , and we had a much easier time getting there!

Eliminate the parentheses and combine like-terms.

Combine all the terms.

The answer is:

When adding trinomials we combine together coefficients of like terms.

Combine like terms:

Factor the numerator and denominator:

Cancel the factors that appear in both the numerator and the denominator:

In order to divide, we must first factor both trinomials on the numerator and denominator.

Notice that we now have common terms in the numerator and denominator that can be divided and cancelled.

Cancel the terms in the numerator and denominator.

The answer is:

Factor both trinomials on the top of the numerator and denominator.

Notice that both the top and bottom share the term, which can be eliminated.

The answer is:

In order to simplify this, we will need to factorize the numerator and denominator.

Then, .

Simplify the common terms in the numerator and denominator.

The answer is:

Factor out the 7:

Take the 8 from the x-term, cut it in half to get 4, then square it to get 16. Make this 16 equal to C/7:

Solve for C:

To factor trinomials like this one, we need to do a reverse FOIL. In other words, we need to find two binomials that multiply together to yield .

Finding the "first" terms is relatively easy; they need to multiply together to give us , and since only has two factors, we know the terms must be and . We now have  , and this is where it gets tricky.

The second terms must multiply together to give us , and they must also multiply with the first terms to give us a total result of . Many terms fit the first criterion. , , and all multiply to yield . But the only way to also get the "" terms to sum to is to use . It's just like a puzzle!

For the trinomial to be factorable, we would have to be able to find two integers with product 36 and sum ; that is, would have to be the sum of two integers whose product is 36.

Below are the five factor pairs of 36, with their sum listed next to them. must be one of those five sums to make the trinomial factorable.

1, 36: 37

2, 18: 20

3, 12: 15

4, 9: 13

6, 6: 12

Of the five choices, only 16 is not listed, so if , then the polynomial is prime.