Step 1: Find factors of 44:



Step 2: Find which pair of factors can give me the middle number. We will choose.

Step 3: Usingand, we need to get. The only way to getis if I haveand.

Step 4: Write the factored form of that trinomial:



Step 5: To solve for x, you set each parentheses to:




The solutions to this equation areand.

Step 1: Factor by pairs:





第二步:重写factorization:



Step 3: Solve for x:

Step 1: Find two numbers that multiply toand add to.

We will choose.

Step 2: Factor using the numbers we chose:



Step 3: Solve each parentheses for each value of x..

Based upon the fundamental theorem of algebra, we know that there must exist 3 roots for this polynomial based upon its' degree of 3.

To solve for the roots, we use factor by grouping:

First group the terms into two binomials:

Then take out the greatest common factor from each group:

Now we see that the leftover binomial is the greatest common factor itself:

We set each binomial equal to zero and solve:

我n order to find the roots for the polynomial we must first put it in Standard Form by decreasing exponent:

Now we can use factor by grouping, we start by grouping the 4 terms into 2 binomials:

We now take the greatest common factor out of each binomial:

We can see that each term now has the same binomial as a common factor, so we simplify to get:

To find all of the roots, we set each factor equal to zero and solve:

Step 1: Find two numbers that multiply toand add to...

We will choose

Check:




We have the correct numbers...

Step 2: Factor the polynomial...



Step 3: Set the parentheses equal to zero to get the roots...

So, the roots are.

我n order to find the roots of the polynomial we must factor by grouping:

Group into two binomials:

Take out the greatest common factor from each binomial:

We can now see that each term has a common binomial factor:

We set each factor equal to zero and solve to obtain the roots:

Step 1: Evaluate.



Step 2. Evaluate

从之前的年代tep, we already know whatis.

is just multiplying by another




Step 3: Evaluate.

The expansion ofis

Solution:

We can look at Pascal's Triangle, which is a quick way to do Binomial Expansion. We read each row (across, left to right)

For the first row, we only have a constant.
For the second row, we get.
...
For the 7th row, we will start with anterm and end with a constant.

Step 1: We need to locate the 7th row of the triangle and write the numbers in that row out.

The 7th row is.

Step 2: If we translate the 7th row into an equation, we get:

. This is the solution.