Your SlideShare is downloading.
×

×
# Saving this for later?

### Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime - even offline.

#### Text the download link to your phone

Standard text messaging rates apply

Like this presentation? Why not share!

- Operations on Polynomials by Jeramy Donovan 4857 views
- Polynomials by Madhavi Mahajan 3299 views
- Polynomials by Divyanshu Saxena 2433 views
- 1.3 Multiplying Polynomials by Mrs. LaPage 40 views
- Topic 1 adding & subtracting poly... by Annie cox 1194 views
- Polynomials by rljohnson68 36 views
- Special Products by deathful 295 views
- Review of multiplying polynomials by dlaughter 632 views
- Multiplying polynomials by NCVPS 1660 views
- March 4, 2015 by khyps13 244 views
- March 6, 2015 by khyps13 239 views
- 6.5 polynomials (1) by 9047845727 395 views

Like this? Share it with your network
Share

2,785

views

views

Published on

adding, subtracting, and multiplying polynomials

adding, subtracting, and multiplying polynomials

No Downloads

Total Views

2,785

On Slideshare

0

From Embeds

0

Number of Embeds

3

Shares

0

Downloads

59

Comments

0

Likes

1

No embeds

No notes for slide

- 1. Unit 3 PolynomialsAdding PolynomialsSubtracting PolynomialsMultiplying PolynomialsBy Genny Simpson
- 2. Let’s Review!Integer rulesExponent rulesCombining like-terms
- 3. Before you can add or subtract polynomials you need to review theinteger 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 largernumber. For instance 10 + -6 = 4 and -10 + 6 = -4.To subtract integers, change the subtraction sign to adding theopposite and then follow the rules for addition. For instance -2 – 3 =-2 + -3 = -5 and 6 – (-5) = 6 + 5 = 11. INTEGER RULES
- 4. The only rule we really need for now is the multiplication rule.W hen you multiply bases, you multiply the numbers in front, thecoefficients, and add the exponents.For example: 3x · 2x = 6x2 and 4x2 · 5x = 20x3.EXPONENT RULES
- 5. To combine like terms they must be the same except for thenumbers 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 differentsigns. Subtract 3 from 5 and keep the negative or -2x.To combine 2y3 and 7y3, use the addition rule for integers: samesigns, add and keep the sign. So 2y3 + 7y3 = 9y3.To combine -2x2 and 9x2, you use the addition rule again, subtractand keep the sign of the larger number. So -2x2 + 9x2 = 7x2.COMBINING LIKE TERMS
- 6. To add polynomials, we are using the integer rules for addition andsubtraction and combining like terms.For example: (2x2 – 3x + 5) + (4x2 + 5x – 6) Put like terms togetherand combine them. (2x2 + 4x2) + (-3x + 5x) + (5 - 6 ) = 6x2 + 2x – 1.Here’s another example: (5d – 2d2 + 6) + (5d2 + 2). Rearrange tokeep like terms together. Be sure to bring the sign in front of theterm with it when you rearrange. (-2d2 + 5d2) + 5d + (6 + 2).So the answer is 3d2 + 5d + 8.ADDING POLYNOMIALS
- 7. To subtract polynomials, we use the integer rules for addition andsubtraction and combining like terms as well as the distributiveproperty.For example: (6c2 – 2c – 7) – (3c2 – 6c + 1). Before we rearrangeto put like terms together, we need to distribute the negativethrough 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.SUBTRACTING POLYNOMIALS
- 8. There are two methods we can use to multiplypolynomials, the distributive property and the boxmethod.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 + 4xThen distribute by 2. 2 · x2 + 2 · -3x + 2 · 4 = 2x2 – 6x + 8.Now all we do is combine like terms: x3 – x2 – 2x + 8.MULTIPLYINGPOLYNOMIALS
- 9. 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 rowsand three columns. We label the rows with terms of the binomialand the columns with the terms of the trinomial. It looks like this: x2 -2x +7 2x 2x3 -4x2 14x +3 3x2 -6x 21 Notice that the like terms are on the diagonals. So the answer is 2x3 – x2 + 8x + 21.MORE MULTIPLICATION
- 10. 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)
- 11. Template Provided By www.animationfactory.com500,000 Downloadable PowerPoint Templates, Animated Clip Art, Backgrounds and Videos

Be the first to comment