Algebra 2 1.21 Add, Subtract, Multiply Polynomials

Algebra 2 1.21 Add, Subtract, Multiply Polynomials

WARM UP

Multiple Choice

(x + 5)²

Hint: What does it mean to square a number or term?

• x² + 25

• x² + 10x + 25

• x² + 10 x + 10

• x² + 10

Multiple Choice

Factor: x² – 5x – 24

• (x - 5)(x + 19)

• (x - 8)(x + 3)

• (x - 3)(x + 8)

• (x - 19)(x + 5)

Multiple Choice

Factor the Trinomial:

x² - 8x + 15

• (x + 5) ( x + 3)

• (x - 5) (x - 3)

• (x + 15) (x - 1)

• (x - 7) (x - 8)

Learning Targets:

1. I can identify a polynomial and name it's key parts.

2. I can classify a polynomial by degree and number of terms

3. I can write polynomials in standard form

Some Basic Facts...

Read Carefully- You have 30 secs for each question...

Multiple Choice

A symbol for an unknown value is called a _______________. It is usually a letter such as a, X or Y.

• Constant
• Coefficient
• Operator
• Variable

Multiple Choice

A number on its own that does not change and is without a variable is known as a _______________.

• Term
• Variable
• Coefficient
• Constant

Multiple Choice

What is the constant term of:
14 - 8x - 7y

• -8
• -7
• 14
• none

Multiple Choice

What are the coefficients of:
12 - 8x + 14y

• -8x, 14y
• 12, -8, 14
• -8, 14
• 12, -8x, 14y

Multiple Choice

Which expression contains exactly 3 terms?

• 5 + 6xy
• 9 + 4t
• 8 + 2y - 5x
• 24xy

Multiple Choice

What are the terms of:

3x - 2y + 4

• 3x, 2y, 4

• 3x, -2y, 4

• 3x, -2y

• 3x, 2y

Multiple Choice

things that are being multiplied or divided in an expression

• term

• variable

• factor

• coefficient

Multiple Choice

What are the factors of:

4 - 2y

• -2 & y

• 4

• 4; -2 & y

• 4, -2y

Multiple Choice

Which expression includes 2 coefficients?  

• 2x - 4
• 8x + 2
• 23f - 9 + 16
• 3h + 5j -4

Multiple Choice

What is the coefficient of x?

9 - x

• 0

• 1

• -1

• 8

Multiple Choice

Classify:
6x³+3x²+2x−4

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

Classify:
2n³

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

Classify by number of terms:
3x² – 8x + 1

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
3x³ – 6x

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by degree of polynomial:

9x

• Constant

• Linear

• Quadratic

• Cubic

Multiple Choice

Classify by degree of polynomial:

7x²y +5xy - 2

• Constant

• Linear

• Quadratic

• Cubic

Multiple Choice

Classify by degree of polynomial:
2x – 9

• Constant
• Linear
• Quadratic
• Cubic

Multiple Choice

Classify by degree of polynomial:
3x³ – 6x

• Constant
• Linear
• Quadratic
• Cubic

Multiple Choice

If the degree is 0, the type is...

• quadratic

• linear

• cubic

• constant

• quartic

Multiple Choice

9x⁴

• Quadratic polynomial

• Quartic monomial

• Quadratic monomial

• Cubic monomial

Multiple Choice

Classify this polynomial by its degree and number of terms:  x² + 2x + 6

• Linear polynomial
• Quadratic trinomial
• Quadratic binomial
• Cubic trinomial

Multiple Choice

Classify this polynomial by its degree and number of terms:  x² + 6

• Linear polynomial
• Quadratic trinomial
• Quadratic binomial
• Cubic binomial

Multiple Choice

f(x)=3x + 3x² − 0.1x³ + 0.5

• Yes, it is a polynomial function.

• No, it is not a polynomial function.

Multiple Choice

Is it a polynomial?

• yes

• no

Multiple Choice

f(x)=10x⁷ −9+6x^y -10x

• Yes, it is a polynomial function.

• No, it is not a polynomial function.

Multiple Choice

g(x)=3x² − 1x^-4 + 7

• Yes, it is a polynomial function.

• No, it is not a polynomial function.

Multiple Select

Which ones are polynomials? (You may select more than one.)

Look at the last example very closely!

Multiple Choice

True or false?

To find the leading coefficient, we have to write our polynomial so that the order of the degree goes from least to greatest?

• true

• false

Multiple Choice

Write the polynomial so that the powers of x are in descending order, -3x + 8x² - 11 + 9x³

• It is already in standard form

• 9x³ + 8x² - 3x - 11

• 8x² + 9x³ -11 - 3x

• -11 - 3x + 8x² + 9x³

Multiple Choice

Which polynomial is written in standard form?

• -3x + 8x² + 9x³ - 11

• 9x³ + 8x² - 3x - 11

• 8x² + 9x³ -11 - 3x

• -11 - 3x + 8x² + 9x³

Multiple Choice

Put in Standard Form.
12 - 3x³ - 10x - x²

•  - 3x³ - x² - 10x + 12
•  3x³ - x² + 10x + 12
• 12 - 3x³ - 10x - x²
  It is in Standard Form.
• 12 - 10x - 3x³ - x²

Multiple Select

Which of these is in Standard Form?

•  $4x^2+12x-13x^3$  

•  $5-3x$  

•  $2x^4-12x^2+5x-9$  

•  $5x^5+4x^{\text{4}}+12x^3-23x+15$  

Learning Targets:

1. I can add and subtract polynomials and write result in standard form.

2. I can multiply polynomials and write result in standard form.

Multiple Choice

ADD:

(4x³-5x²+3x)+(-2x³-x²+6x)

• 2x³-6x²-9x

• 2x³+6x²+9x

• -2x³-6x²+9x

• 2x³-6x²+9x

Multiple Choice

SUBTRACT

(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

• 4b⁴ - 2b³ + 7

• 5b⁴ - 2b³ + 4

• b⁴ - 2b³ + 7

• 5b⁴ - 2b³ + 7

Multiple Choice

Find the product:

(5n-8)(5n+8)

• 25n²-64

• 10n²

• 5n²+16

• 16

Multiple Choice

(n² + 6n − 4)(2n − 4)

• 2n³ + 16n² − 32n + 16

• 2n³ + 8n² − 32n + 16

• 2n³ + 8n² − 12n + 16

• 2n³ + 8n² − 32n - 16