4/15 - Operations with Polynomials

​3 min

​3 min

Categorize

Options (13)

$$x$$  

$$x^2$$  

$$-x$$  

$$\left(x\cdot7x\right)$$  

$$\left(3x-7x\right)$$  

$$4x^2$$  

$$3$$  

$$0x^2$$  

$$\left(x-x\right)$$  

Add

Subtract

Multiply

Divide

Sort the following terms into the correct category.

Simplify terms before categorizing. (7 min)

"x" term

"x squared" term

Math Operations

constant term

LO:

SWBAT add, subtract, and multiply polynomials.

DOL: Given 5 problems, students will correctly add,

subtract, and multiply polynomials in at least
4 of 5 questions.

2

ALGI.10A - Add and subtract polynomials of degree one and degree two.

ALGI.10B - Multiply polynomials of degree one and degree two.

​1 min

Lesson Vocabulary

3

Polynomial

7x²+ 3x + 1

Monomial

Ex: 5x, 8 , 3x²

Binomial

Ex: 4x⁴ + 9

Trinomial

Ex: 9x² + 7x − 13

Constant

Ex: 23, 6, −13

1 term

2 terms

3 terms

Contains no variables

Coefficient

Constant

Term

​1 min

Constants

x Terms

x² Terms

5

Do Now Revisit

Most of the terms in the Do Now were monomials.

x

x²

3

−5x

2x

9x

−x

(x − x)

16
10x²

−7x²

(3x − 7x)
(x · 7x)
0x²

The binomial expressions could be
simplified as monomials because they were combinations of
like terms.

● (x − x) = 0
● (3x − 7x) = −4x

Other expressions were more complex monomials that still had to be simplified before being categorized.

● 0x² = 0
● (x · 7x) = 7x²

2 min

Multiple Choice

Which of the following expressions are already simplified? (3 min)

• $$-2x^2+8x^2$$

• $$5x-9x$$

• $$-23x+8x^2$$

Math Response

(4 min) Simplify the following expression:

$$-2x^2+8x^2$$

Type answer here

Correct Answer: 6x^2

Deg^°

Rad

7

Adding/Subtracting Polynomials

To combine larger polynomials we need a way to group the like terms together.

(3x² + 11x − 39) + (−x² + 8x + 5)

Vertical Grouping

+

(3x² + 11x − 39)
(−x² + 8x + 5)

2x² + 19x − 34

​3 min

8

Adding/Subtracting Polynomials

When subtracting, you can reverse the signs in the subtracted polynomial.

(7x² − 2x + 51) − (5x² + 15x − 8)

Vertical Grouping

−

(7x² − 2x + 51)
(5x² + 15x − 8)

2x² − 17x + 59

Or +

(7x² − 2x + 51)
(-5x² - 15x + 8)

2x² − 17x + 59

​3 min

9

Think - Pair - Share

Sara wants to build a new flower garden and has decided on the following
dimensions. Which equation would help her decide how much wood to use for the
perimeter of the flower garden?

​You have 3 minutes to discuss with your partners how you would approach this problem.

​5 min

Multiple Choice

Sara wants to build a new flower garden and has decided on the following dimensions. Which equation would help her decide how much wood to use for the perimeter of the flower garden? (5 min)

• $$4x^2+5x+7$$

• $$8x^2+10x+14$$

• $$20x^2+27x−8$$

• $$20x^3+32x^2−5x−8$$

Math Response

Lap 1 - 5 min

Simplify the following expression on your whiteboard:

$$(x^2+7x+18)+(4x^2−5x−12)$$

Type answer here

Correct Answer: 5x^2+2x+6

Deg^°

Rad

Math Response

Lap 2 - 5 min

Simplify the following expression on your whiteboard:

$$(x^2+12x+25)−(5x^2+x−20)$$

Type answer here

Correct Answer: -4x^2+11x+45

Deg^°

Rad

11

Multiplying Polynomials

The basic principle of multiplication is that each term of the first polynomial has to be multiplied by each term of the second polynomial.

(4x − 3)(7x + 2)

A grid is a good way to organize this kind of multiplication.

4x

−3

7x

2

​5 min

12

Multiplying Polynomials

How would you arrange a grid to solve the following multiplication problem?

(b² + 2b − 9)(−5b + 6)

−5b

6

b²

2b

−9

​5 min

9

Think - Pair - Share

Sara is trying to fill the flower garden she built. Which equation could she used to help determine how much dirt she need to fill the flower garden?

​You have 3 minutes to discuss with your partners how you would approach this problem.

​5 min

Multiple Choice

Lap 3 - 5 min

Sara is trying to fill the flower garden she built. Which equation could she used to help determine how much dirt she need to fill the flower garden?

• $$4x^2+5x+7$$

• $$8x^2+10x+14$$

• $$20x^2+27x−8$$

• $$20x^3+32x^2−5x−8$$

Dropdown

​

Select answer

have the ​

Select answer

variables and exponents along with a coefficient. Like terms can be ​

Select answer

by adding or subtracting the coefficients. (3 min)

DOL: Given 5
problems, students
will correctly add,
subtract and multiply
polynomials in at least 4 of
5 questions.

17

Demonstration of Learning

Open Ended

• How do you simplify the sum, difference, or product of polynomials?

• Use complete sentences: You can simply polynomials by ...