CCGPS AlgebraDay 30 (9-18-13)

UNIT QUESTION: In what ways can algebraic methods be used

in problems solving?Standard: MCC9-12.N.RN.1-3, N.CN.1-3, A.APR.1

Today’s Question:What methods can we use to

multiply polynomials?Standard: MCC9-12.A.APR.1

Objective: To classify polynomials by degree and by number of terms

Classifying Polynomials

Example of a Polynomial

5364 23 xxx

Coefficients

Degrees

Constant

Vocabulary

Degree: is the exponent for each variable.

Degree of the polynomial: is the largest exponent of the polynomial.

Leading coefficient: is the coefficient of the first term.

Descending order/Standard form is how polynomials are written where the terms are placed in descending order from largest degree to smallest.

Classifying Polynomials By Degree

Degree Example Example

Constant 0 6 -3

Linear 1 3x + 4 -7x + 2

Quadratic 2 123 2 xx 46 2 x

Classifying polynomials By # of terms

# of terms Example Example

Monomial 1 3x 27x

Binomial 2 3x + 1 xx 28 3 Trinomial 3 523 26 xx 534 2 xx

Note: Any polynomials with four or more terms are just called polynomials

Multiplying Polynomials

Monomial x Polynomial

(5)(x + 6)

5 30x

(x2)(x + 6)

3 26x x

Multiplying Polynomials

Binomial x Binomial

Genetics

Punnett Squares are diagrams used by scientists to help them to figure out how inherited traits (characteristics) will be distributed.

F

f

f

f

Ff

Ff

ff

ff

We will use something like a Punnett Square today to help us learn how to multiply polynomials!!

Multiplying Polynomials

Using the distributive property

Notes - Multiplying Polynomials

F - First

O - Outside

I – Inside

L - Last

(z + 5) (z + 3)

(x - 2) (x + 4)

2 2 8x x

(x + 9) (x – 3)

2 6 27 x x

(x + 3) (x – 3)

2 27x 9

(2x + 5)(x + 6)

22 17 30 x x

(3x – 1)(2x – 4)

26 14 4 x x

Find the area of the rectangle.

228 96 80 x x

7 10x

4 8x

Find the area of the rectangle.

25 21 4 x x

4x

5 1x

HomeworkPractice

Worksheet

12-2-13 Closer

1. (2x2)(-4x3)

2. 2(x + 4)

3. 7(12 + 3x) – 10

2x + 8

-8x5

21x + 74