Factoring:Greatest Common Factor

There is a factoring that is easier than FOIL and that is called the GCF or the Greatest Common Factor. The greatest common factor is a number that divisible by a set of numbers. For instance, the gcf of 12 and 18 is 6 because 12/6 = 2 and 18/6 = 3.

Well, what if there isn’t any coefficients? What if there is only variables and exponents? The same rules apply. For example, if I were to find the greatest common factor between x^3 and x^2, I must factor each term and eliminate my Xs.

ex.  x^3=  x* x* x    and x^2 = x * x

eliminate  x*x*x and x*x

The greatest common factor between these two terms is x^2.

Remember the factor BOX that Ms. Umeh showed in class?

First box: first term

Second box: second term

Third box: third term

If your middle term is a negative, your operations when you factor must also be negative. If your last term is negative, then your operations must be addition and subtraction.

 

If you need additional help, come to lunch tutoring.

Section 8.3 Dividing Monomials and Raising a Power to a Power

Section 8.3 Dividing Monomials and Raising a Power to a Power

Things to Remember

Dividing Monomials

In dividing monomials, there are two things that you must keep in mind. First, you divide your coefficients, which are the numbers that are written before the variables. As for the exponents (the powers), you would subtract them.

ex.   bases stay the same. subtract the exponents (9 – 3 = 6)

1000000 (count the number of zeros) There are six zeros, which means that your final answer is  .

Raising a power to a power

When you raise a power to a power, you are multiplying the two exponents together. For instance, a variable raised to the 5th power and then to the 2nd power would result in that variable raised to the 10th power. However, when you are raising a coefficient to an exponent, you would multiply the coefficient by the number of times represented as the exponent. So, y raised to the 7th power then raised to the 3rd power is the same as saying 7 *7 * 7 .

SYSTEM OF LINEAR EQUATIONS

Determine the solution set of a system of inequalities by following these five steps.

1. Put your linear inequalities into slope-intercept form
2. Determine whether your lines will be dashed (—–) or solid (——)
3. Graph your linear inequalities
4. Select a test point (such as (0, 0) to determine if the linear inequality is true or false
5. Shade the TRUE side of the line

y < – x + 4

GRAPHIING S.O.E. 2

x – 13 = 2y + x – 17          FIRST EQUATION

3x + y= 29                           SECOND EQUATION

Step 1: Take the 2nd equation and put it into y-intercept form.

3x – 3x + y = 29 – 3x——-> y  =-3x + 29

Step 2: Substitute the above equation for y in the 1st equation.

x – 13 = 2(-3x + 29) + x – 17 ——>     x- 13 = -6x + 58 + x -17 ——>  x – 13 = -5x + 41  ——> x + 5x – 13 = -5x + 5x + 41

6x – 13 = 41 —–> 6x = 54 —-> 6x/6 = 54/6 —–> x = 9

Step 3: Substitute your x-value into the second equation.

3(9) + y = 29 —–> 27 + y = 29 —–> 27- 27 + y = 29 – 27 ——> y = 2

Step 4: Write your solution.

Solution (9, 2)