### Present Remotely

Send the link below via email or IM

CopyPresent to your audience

Start remote presentation- Invited audience members
**will follow you**as you navigate and present - People invited to a presentation
**do not need a Prezi account** - This link expires
**10 minutes**after you close the presentation - A maximum of
**30 users**can follow your presentation - Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

### Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.

You can change this under Settings & Account at any time.

# Polynomials

You Teach Project - Algebra

by

Tweet## Camille Jean

on 10 January 2013#### Transcript of Polynomials

Polynomials Warm - Up! Determine whether each term is a monomial or not.

1) 10

2) h+i

3) -b

4) 56 Polynomials *Polynomial: Is a monomial or a sum of monomials.(Ex. 3n +2d + 3j +2c + 3c) Degree - Example *Monomial is a number, variable, or a product of a number and 1 or more variable(s). Definitions: *Binomial: The sum of two monomials.

(Ex. 3b + 6a) *Trinomial: The sum of three monomials.

(Ex. c + 2a + 3t) *Degree of a Polynomial: The greatest degree (exponent) of any term in the polynomial. Ex. 1 *Degrees are always in a descending order.

Ex.: -4x y + 3x + 5 2 2 2 4 2 *4 is the largest exponent so it's the degree of the polynomial Ex. 2 9y 1 *If there is no exponent written then it is to the power of one 6h - h + p + p 4 3 2 *In one term you add all exponents for the total degree Adding Polynomials-Example *To add polynomials line up the like terms and add, or group like terms together. Watch... Ex. 1 (4x - 5x + 9) + (3x + 4x + 3)

Way 1: Horizontal

(4x + 4x ) + (-5x + 3x) + (9 + 3)

=8x - 2x + 12 2 2 2 2 Way 2: Vertical

4x - 5x + 9 2 + 4x + 3x+ +3 2 8x - 2x + 12 2 2 *Group the like terms. *Add like terms * The polynomials are in descending degree order. * Align like terms and add. Subtracting Polynomials - Example Ex. 1 (4n + 7n + 5n) - (3n + 6n)

Way 1: Horizontal 3 2 3 Way 2: Vertical

7n + 4n + 5n - 3n + 6n 3 2 3 *Align like terms and subtract 7n + n - n 3 2 Multiplying polynomials by a monomial Multiplying polynomials not

7h + 3p + 67 3 7n + (4n - 3n ) + (5n - 6n) 2 3 3 *Group like terms = n + 7n - n 2 3 Ex. 1 -4x(2x - 6x + 15) Way 1: Horizontal -4x(2x) - -4x(6x) + -4x(15) =-8x + 24x - 60x Way 2: Vertical (2x - 6x + 15) = 16x - 60x x -4x 16x - 60x *Monomial *Polynomial "Foil" Method (x + 4)(x - 6) = x(x - 6) + 4(x - 6) *Distributive property =x - 6x + 4x - 24 2 *Solve =x - 2x - 24 2 *Simplify Ex. 1 Steps: F - First terms

O - Outer terms

I - Inner terms

L - Last terms

(x + 4)(x - 3) Outer Inner First Last *This makes it easier to multiply polynomials. Any questions about Degree, Subtracting, Adding, Multiplying polynomials, or the FOIL method? *Distributive property Steps: *Solve and simplify *Solve (descending egree) Steps: *Complete the homework worsheet. 1/11/13 *Once you multiply each term according to FOIL, write out the equation and simplify You try:

(2x + 8)(x - 2) You try:

(x + 4)(2x - 3) You try:

-2x(x + 10) You try:

1) (2x - 5) - (x + 4)

2) (3x + 5) + (x + 2) Answers:

1) Yes

2) No

3) Yes

4) Yes * Rearrange degrees in descending order. = n + 7n - n 3 2 Answers:

1) (x - 9)

2) (4x + 7) Answer:

-2x - 20x 2 2 2 2 2 Answer:

2x + 5x - 12 2 Answer:

2x + 4x - 16 2

Full transcript1) 10

2) h+i

3) -b

4) 56 Polynomials *Polynomial: Is a monomial or a sum of monomials.(Ex. 3n +2d + 3j +2c + 3c) Degree - Example *Monomial is a number, variable, or a product of a number and 1 or more variable(s). Definitions: *Binomial: The sum of two monomials.

(Ex. 3b + 6a) *Trinomial: The sum of three monomials.

(Ex. c + 2a + 3t) *Degree of a Polynomial: The greatest degree (exponent) of any term in the polynomial. Ex. 1 *Degrees are always in a descending order.

Ex.: -4x y + 3x + 5 2 2 2 4 2 *4 is the largest exponent so it's the degree of the polynomial Ex. 2 9y 1 *If there is no exponent written then it is to the power of one 6h - h + p + p 4 3 2 *In one term you add all exponents for the total degree Adding Polynomials-Example *To add polynomials line up the like terms and add, or group like terms together. Watch... Ex. 1 (4x - 5x + 9) + (3x + 4x + 3)

Way 1: Horizontal

(4x + 4x ) + (-5x + 3x) + (9 + 3)

=8x - 2x + 12 2 2 2 2 Way 2: Vertical

4x - 5x + 9 2 + 4x + 3x+ +3 2 8x - 2x + 12 2 2 *Group the like terms. *Add like terms * The polynomials are in descending degree order. * Align like terms and add. Subtracting Polynomials - Example Ex. 1 (4n + 7n + 5n) - (3n + 6n)

Way 1: Horizontal 3 2 3 Way 2: Vertical

7n + 4n + 5n - 3n + 6n 3 2 3 *Align like terms and subtract 7n + n - n 3 2 Multiplying polynomials by a monomial Multiplying polynomials not

7h + 3p + 67 3 7n + (4n - 3n ) + (5n - 6n) 2 3 3 *Group like terms = n + 7n - n 2 3 Ex. 1 -4x(2x - 6x + 15) Way 1: Horizontal -4x(2x) - -4x(6x) + -4x(15) =-8x + 24x - 60x Way 2: Vertical (2x - 6x + 15) = 16x - 60x x -4x 16x - 60x *Monomial *Polynomial "Foil" Method (x + 4)(x - 6) = x(x - 6) + 4(x - 6) *Distributive property =x - 6x + 4x - 24 2 *Solve =x - 2x - 24 2 *Simplify Ex. 1 Steps: F - First terms

O - Outer terms

I - Inner terms

L - Last terms

(x + 4)(x - 3) Outer Inner First Last *This makes it easier to multiply polynomials. Any questions about Degree, Subtracting, Adding, Multiplying polynomials, or the FOIL method? *Distributive property Steps: *Solve and simplify *Solve (descending egree) Steps: *Complete the homework worsheet. 1/11/13 *Once you multiply each term according to FOIL, write out the equation and simplify You try:

(2x + 8)(x - 2) You try:

(x + 4)(2x - 3) You try:

-2x(x + 10) You try:

1) (2x - 5) - (x + 4)

2) (3x + 5) + (x + 2) Answers:

1) Yes

2) No

3) Yes

4) Yes * Rearrange degrees in descending order. = n + 7n - n 3 2 Answers:

1) (x - 9)

2) (4x + 7) Answer:

-2x - 20x 2 2 2 2 2 Answer:

2x + 5x - 12 2 Answer:

2x + 4x - 16 2