Factor:

Step 1: Factor out

Step 2: Factor the polynomial

Factor:

When factoring a polynomial, the product of the coefficients must be, the sum of the factors must be, and the product of the factors must be.

For the above equation,,, and.

Set up the factor equation:

Becauase是负的,的一个因素must be negative as well. Becauseis positive, this means the larger factor is positive as well.

Two numbers that meet these requirements areand. Their product is, and their sum is.

Follow the FOIL rule when multiplying - first, outside, inside, last.

First:

Oustide:

Inside:

Last:

一个dd all of these together:

Combine like terms:

Subtract 12 from both sides:

Factor:

Then, by the zero-product property,

or.

Solve:

or

Factor:

The last term is positive, which indicates that both factors should be positive:

The sum of the factors must be, and their product must be.

This means the factors areand

Therefore:

When factoring trinomials with larger coefficients, rather than guess and check, there is a 4 step process that will always yield a correct answer.

Step 1- Multiply the first and third terms

Step 2- Find two factors that multiply to equal the result of step 1 () and add up to equal the second/middle term.

The productand

Their sum isThis works!!

So,andare our new factors

Step 3- Replace our middle term () with our two new factors.

Step 4- Factor by grouping to find your answer

一个nswer!!!

To check your work, FOIL, and see if you get our original trinomial

This can be solved by looking at all of the answers and multiplying them and comparing to the answer. However this is time consuming. You can start by noting that the termcan be a result of, where one of the terms is negative, so one answer can be eliminated. It is also clear thatmust be the result ofmultiplied by, so two additional answers can be eliminated. Looking at the last two answers and multiplying through, the correct answer can be determined.

The polynomial factors into (x + 3) (3x - 2).

3x² + 7x – 6 = (a + b)(c + d)

There must be a 3x term to get a 3x² term.

3x² + 7x – 6 = (3x + b)(x + d)

The other two numbers must multiply to –6 and add to +7 when one is multiplied by 3.

b * d = –6 and 3d + b = 7

b = –2 and d = 3

3x² + 7x – 6 = (3x – 2)(x + 3)

(x + 3) is the correct answer.

The product of the last two numbers should be 6, while the sum of the products of the inner and outer numbers should be 5x. Factors of six include 1 and 6, and 2 and 3. In this case, our sum is five so the correct choices are 2 and 3. Then, our factored expression is (x + 2)(x + 3). You can check your answer by using FOIL.

y = x²+ 5x + 6

2 * 3 = 6 and 2 + 3 = 5

(x + 2)(x + 3) = x²+ 5x + 6

You can set the two numbers to equal variables, so that you can set up the algebra in this problem. The first odd number can be defined asand the second odd number, since the two numbers are consecutive, will be.

This allows you to set up the following equation to include the given product of 195:

Next you can subtract 195 to the left and set the equation equal to 0, which allows you to solve for:

你可以二次装备的因素ation by determining which factors of 195 add up to 2. Keep in mind they will need to have opposite signs to result in a product of negative 195:

Set each binomial equal to 0 and solve for. For the purpose of this problem, you'll only make use of the positive value for:

Now that you have solved for, you know the two consecutive odd numbers are 13 and 15. You solve for the answer by finding the sum of these two numbers: