The first step in setting up our binomial is to figure out our possible leading terms. In this case, the only reasonable factors of  are :

Next, find the factors of . In this case, we could have  or . Since the factor on our leading term is , and no additive combination of  and   or of  and  can create our middle term of , we know that our factors must be .

Note that since the last term in the ordered trinomial is positive, the factors must have the same sign. Since the middle term is negative, both factors must have a negative sign.

Therefore, we have one possibility, .

Let's solve, and check against the original triniomial, before solving for .

Thus, our factors are  and .

Now, let's solve for . Simply plug and play:

Therefore,  and .

Note that, in algebra, we can represent this by showing . However,  writing the word "and" is perfectly acceptable.

A factored trinomial is in the form , where  the second term and  the third term.

To factor a trinomial you first need to find the factors of the third term. In this case the third term is . 

Factors of  are: 

The factors you choose not only must multiply to equal the third term, they must also add together to equal the second term.

In this case they must equal .

To check your answer substitute the factors of  into the binomials and use FOIL.

First terms: 

Outside terms: 

Inside terms: 

Last terms: 

Simplify from here by combining like terms

Using FOIL returned it to the original trinomial, therefore the answer is:

To factor the trinomial, its general form given by , we must find factors of the product  that when added together give us . 

For our trinomial,  and . The two factors that fit the above rule are  and , because  and .

Using the two factors, we can rewrite the term  as a sum of the two factors added together and multiplied by x:

Now, we must factor by grouping, which means we group the first two terms, and the last two terms, and factor them:

Note that after we factored the two groups of terms, what remained inside the parentheses is identical for the two groups.

Simplifying further, we get

, which is our final answer. 

A perfect square trinomial takes the form

,

where

Since , for  to be a perfect square, 

.

This makes the correct choice.

Set up this problem vertically like you would a normal multiplication problem without variables. Then, multiply the  term to each term in the trinomial. Next, multiply the term to each term in the trinomial (keep in mind your placeholder!).

Then combine the two, which yields:

You can look at this as the sum of two expressions multiplied by the difference of the same two expressions. Use the pattern

,

where  and .

To find , you use the formula for perfect squares:

,

where  and .

Substituting above, the final answer is .

When multiplying these two trinomials, you'll need to use a modified form of FOIL, by which every term in the first trinomial gets multiplied by every term in the second trinomial. One way to do this is to use the grid method.

You can also solve it piece by piece the way it is set up. First, multiply each of the three terms in the first trinomail by . Second, multiply each of those three terms again, this time by . Finally multiply the three terms again by .

Finally, you can combine like terms after this multiplication to get your final simplified answer:

When multiplying this trinomial by this binomial, you'll need to use a modified form of FOIL, by which every term in the binomial gets multiplied by every term in the trinomial. One way to do this is to use the grid method.

You can also solve it piece-by-piece the way it is set up. First, multiply each of the three terms in the trinomail by . Then multiply each of those three terms again, this time by .

Finally, you can combine like terms after this multiplication to get your final simplified answer:

Solving this is just like using FOIL on binomials, except we have nine calculations to perform instead of four (since that's the result of a 3x3 combination!):

First, calculate the combinations of the first term on the left:

Next, calculate the combinations of the middle term on the left:

Next, calculate the combinations of the third term on the left:

Lastly, combine the terms with compatible variables and exponents:

Thus, our answer is .

To solve this problem, first FOIL the binomial.

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

Now, distribute the trinomials. Start with the first term on the left:

Now the middle term on the left:

Now, the third term on the left:

Combine all compatible terms:

Thus,  is our answer.