Intro to Polynomials

Factor the following expression.

1. 5x + 25

Step 1: Find the greatest common factor (GCF). The largest number that divisible by both number is 5. Therefore, your GCF is 5.

Step 2: Factor (break down) your expression into a simpler form. In this case, your factored form is as follows:
5(x + 5).

 

Find the sum or difference of the following polynomial.

(x^3 + 2x + 1) + ( 3x^2 + 4 )

Step 1: If an addition sign is presented, you must find the sum of the polynomial. If a subtraction sign is presented, you must find the difference of the polynomial. In this case, you will find the sum.

Step 2: Combine like terms. Remember, in addition, you cannot combine exponents. All exponents should be written in descending (5, 4, 3,)  order. The only two terms that can be combined in this polynomial is 1 and 4, which will yield a result of 5.

Step 3: Rewrite your expression. Your final answer is x^3 + 3x^2 + 2x + 5.

 

Multiply the following binomial.

When you are multiplying binomials, you can use two methods. The first method is called the FOIL method. FOIL is an acronym for First Outside Inside Last. Another version of FOIL is called the BOX method.

1. (x + 3) (x + 8)            Step 1: Multiply the first terms in both parentheses (x * x = x^2)

Step 2: Multiply the first term in the first parentheses and last term in the second parentheses                                                                     (x * 8 = 8x)

Step 3: Multiply the last term in the first parentheses and the first term in the second parentheses                                                             (3 * x = 3x)

Step 4: Multiply the last terms in both parentheses ( 3 * 8 = 24)

Step 5: Combine the result of Step 2 & 3.

Step 6: Rewrite your final answer.

Your final answer is x^2 + 11x + 24.

 

Find the area of the garden.

Thomasina wants to plant a rectangular rose garden that measures (x + 5) by (6x + 7). What is the area of Thomasina’s rose garden?

Step 1: Write the formula for finding the area of a rectangle. {A = l x w}

Step 2: Substitute your length and width into the formula. {A= (x+5) (6x+7) }

Step 3: Use the FOIL method to multiply the binomial. { A = x^2 +30x + 7x + 35}

Step 4: Combine like terms.  { 30x + 7x = 37x)

Step 5: Write your final answer. { A = x^2 + 37x + 35 }

Multiplying positive/negative binomials with coefficients

Image by wonderferret via Flickr

What is FOIL?’

First   Outside   Inside   Last

There are two methods to use when multiply positive and negative binomials

( x + 7 )  (x – 7 )

How to Graph a Polynomial

The Smiling Man (or Monkey Face) or the Box 

1. Multiply the coefficients for all terms.

2. Combine the outer and inner terms.

Graphing Polynomials

http://www.tabletclass.com

f(x) = x^2 – 2

x:  -3, -2, -1, 0, 1, 2, 3

1. Substitute all of the values that you have for x into the equation

2. Solve for y.

3. Graph.

 

Classwork sheet for wager 3rd prd

Below are photos of the worksheets that will help you study.

TEST 3/17/11- Study tonight- Wager 3rd period

 

Test subject: Monomials, scientific and standard notation, graphing polynomial functions and adding polynomials

CHEAT SHEET- Print this if you can and study before school

Use your classwork sheet as a reference for these explanations below.

Section 1: Perform the operation on the following monomials

*REMEMBER:

(    )   (    ) = multiplication of coefficients only! Add the exponents.

___ = division of coefficients only! Subtract exponents.

If terms are alike, you do subtract/add coefficients. If they are not like terms, you do not do anything with the terms.

Section 2: Perform the operation on the following monomials with no negative or zero exponents.

*REMEMBER:

For dividing monomials-

No exponent means that the variable is raised to the first power! (1 is the exponent)

5g = 5 (g^1) or five times g to the first power

A positive exponent subtracted from a negative exponent

^-6 – (-8) = -6 +8 = -2

Section 3: Write the following numbers in scientific notation

360000000. The decimal place is at the end of the zeros. Move your decimal to the left eight times.

360000000 Rewrite this as 3.6

Everything in scientific notation is written as  x 10 ^power (times ten to the # power).

Section 4: Write the following numbers in standard notation

4. x 10^8    Since the exponent is negative, you would move your decimal place to the opposite direction. When your exponent is positive, move your decimal place to the left.

400000000 There are eight zeros because our exponent is a positive 8.

Section 5: Fill in the table for the following exponential functions and graph the parabolas.

 

 

 

 

 

 

 

 

Section 6: Combine the following polynomials where possible.

* REMEMBER:

Start with the largest exponent and combine them as the operation says.

= 

stays the same.  and are combined .   -5 + 6 = x^4 and -6x^3 stays the same.

 

GOOD LUCK   : )!

Remember, we strive to achieve 80% or more on our tests! Let’s do this.