Unit 3 Polynomials

Adding PolynomialsSubtracting PolynomialsMultiplying Polynomials

By Genny Simpson

Let’s Review!

Integer rulesExponent rulesCombining like-terms

INTEGER RULES

Before you can add or subtract polynomials you need to review the integer rules.

To add integers, add if they have the same sign and keep the sign. For instance -4 + -6 = -10 and 5 + 12 = 17.Subtract if they have different signs and take the sign of the larger number. For instance 10 + -6 = 4 and -10 + 6 = -4.

To subtract integers, change the subtraction sign to adding the opposite and then follow the rules for addition. For instance -2 – 3 = -2 + -3 = -5 and 6 – (-5) = 6 + 5 = 11.

EXPONENT RULES

The only rule we really need for now is the multiplication rule.

W hen you multiply bases, you multiply the numbers in front, the coefficients, and add the exponents.

For example: 3x · 2x = 6x2 and 4x2 · 5x = 20x3.

COMBINING LIKE TERMS

To combine like terms they must be the same except for the numbers in front, the coefficients.

Here are some examples of like terms: 3x and -5x, 2y3 and 7y3, -2x2 and 9x2.

To combine 3x and -5x, you use the integer rule for adding different signs. Subtract 3 from 5 and keep the negative or -2x.

To combine 2y3 and 7y3, use the addition rule for integers: same signs, add and keep the sign. So 2y3 + 7y3 = 9y3.

To combine -2x2 and 9x2, you use the addition rule again, subtract and keep the sign of the larger number. So -2x2 + 9x2 = 7x2.

ADDING POLYNOMIALS

To add polynomials, we are using the integer rules for addition and subtraction and combining like terms.

For example: (2x2 – 3x + 5) + (4x2 + 5x – 6) Put like terms together and combine them. (2x2 + 4x2) + (-3x + 5x) + (5 - 6 ) = 6x2 + 2x – 1.

Here’s another example: (5d – 2d2 + 6) + (5d2 + 2). Rearrange to keep like terms together. Be sure to bring the sign in front of the term with it when you rearrange. (-2d2 + 5d2) + 5d + (6 + 2).So the answer is 3d2 + 5d + 8.

SUBTRACTING POLYNOMIALS

To subtract polynomials, we use the integer rules for addition and subtraction and combining like terms as well as the distributive property.

For example: (6c2 – 2c – 7) – (3c2 – 6c + 1). Before we rearrange to put like terms together, we need to distribute the negative through the second parentheses. (6c2 – 2c – 7) + (-3c2 + 6c - 1).

Now we can rearrange and group like terms. (6c2 + -3c2) + (-2c + 6c) + (-7 – 1) = 3c2 + 4c – 8.

MULTIPLYINGPOLYNOMIALS

There are two methods we can use to multiply polynomials, the distributive property and the box method.

Let’s look first at the distributive property. First distribute by x.

(x + 2)(x2 – 3x + 4) = x · x2 + x · -3x + x · 4 = x3 – 3x2 + 4x

Then distribute by 2. 2 · x2 + 2 · -3x + 2 · 4 = 2x2 – 6x + 8.

Now all we do is combine like terms: x3 – x2 – 2x + 8.

MORE MULTIPLICATION

Now let’s take a look at the Box Method!

To multiply (2x + 3)(x2 – 2x + 7) we need to draw a box with 2 rows and three columns. We label the rows with terms of the binomial and the columns with the terms of the trinomial. It looks like this:

2x

+3

x2 -2x +7

2x3

3x2

-4x2

-6x

14x

21

Notice that the like terms are on the diagonals. So the answer is 2x3 – x2 + 8x + 21.

Now it’s your turn! Practice adding, subtracting, and multiplying polynomials.

1. (4x3 – 2x2 + 5) + (-10x2 + 6x + 7)

2. (-15x2 + 7x – 11) – (-11x2 – 13x + 9)

3. (16x – 13) – (3x2 + 5x – 10) + (7x – 12x2 + 8)

4. 5x3(2x2 – 4x + 15)

5. (3x – 7)(2x + 9)

6. (6x + 5)(3x2 – x – 4)

Template Provided By

www.animationfactory.com

500,000 Downloadable PowerPoint Templates, Animated Clip Art, Backgrounds and Videos