4/15 - Operations with Polynomials

Presentation

•

Mathematics

•

9th Grade

•

Practice Problem

•

Medium

•

CCSS

6.NS.B.3, HSA.APR.A.1, 6.EE.A.4

Standards-aligned

Nicole Richardson

Used 23+ times

FREE Resource

11 Slides • 9 Questions

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.

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

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

Do Now Revisit

Most of the terms in the Do Now were monomials.

x²

−5x

−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

Deg^°

Rad

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

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

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

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

Deg^°

Rad

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.

−3

5 min

Multiplying Polynomials

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

(b² + 2b − 9)(−5b + 6)

−5b

b²

−9

5 min

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

have the

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

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.

Demonstration of Learning

Open Ended

How do you simplify the sum, difference, or product of polynomials?
Use complete sentences: You can simply polynomials by ...

Type response here

3 min

Show answer

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