10-1 Adding and Subtracting Polynomials

10-1 Adding and Subtracting Polynomials

Learning Outcomes

Adds and subtracts polynomials by combining like terms.

Multiple Choice

Classify the polynomial by its number of terms.

4x² - 2

• A

  monomial

• B

  binomial

• C

  trinomial

• D

  polynomial

Multiple Choice

Classify the polynomial by its degree.

x² + 2x³ - 4

• A

  binomial

• B

  trinomial

• C

  quadratic

• D

  cubic

Multiple Choice

Which is an example of a linear polynomial?

• x²-5
• 6x+4
• 5x⁵
• 2x³-9x²

Multiple Choice

What is the leading coefficient of the following polynomial?
5x²-3x+6

• 2
• -3
• 5
• 6

Multiple Choice

Which is an example of a cubic binomial?

• x³+5
• x²+3
• x²+5x-6
• 5x³

Multiple Choice

What is the degree classification of this polynomial?
x²+4x-8

• binomial
• trinomial
• quadratic
• cubic

Multiple Choice

Rewrite the polynomial in standard form: -5 + 4m

• -5 + 4m
  
• 4m - 5
• -4m + 5
• 4m² - 5

Multiple Choice

Polynomial or not?

• polynomial
• not a polynomial

Multiple Choice

Polynomial or not?
5x⁴ - 7x

• polynomial
• not a polynomial

Multiple Choice

Classify by the DEGREE:

3x - 2

• 1

• 2

• 3

• 4

Multiple Choice

Classify

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Select

Which of these is in Standard Form?

•  $4x^2+12x-13x^3$  

•  $5-3x$  

•  $2x^4-12x^2+5x-9$  

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

Multiple Choice

Name and Classify the Polynomial:
x² − 4

• quadratic binomial
• quadratic monomial
• linear binomial
• linear monomial

Multiple Choice

When a polynomial is written in standard form, the coefficient of the first term is called the _____________.

• Boss coefficient
• Leading coefficient
• Best coefficient
• Greatest common coefficient

Multiple Choice

Classify by the DEGREE:
4x³ - 5x² + 2x - 1

• Degree of 1
• Degree of 2
• Degree of 3
• Degree of 4

Multiple Choice

What id the Degree of the Polynomial?
5x³ - 6x + 1

• Linear 
• Quadratic
• Cubic
• Quartic

Multiple Choice

What is the leading coefficient? 
f(x)=5x²+3x³-2x+1

• 5
• 3
• -2
• 1

Multiple Choice

What is the leading coefficient in the polynomial 3x²-2x+5?

• 3
• 2
• 5
• 0

Multiple Choice

What is the constant in the polynomial x²-2x+5?

• 1
• 2
• 5
• 0

Multiple Choice

Add the polynomials (x-2) and (x²+3)

• x²+x+1

• x³+5

• x³+1

• x³-1

Multiple Choice

Simplify each expression.

(6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

• 11x⁴ + 2x² + 14x

• 16x⁴ + x² + 14x

• 11x⁴ + x² + 14x

• 11x⁴ + 2x² + 10x

Multiple Choice

Combine like terms to simplify:

(5x + 2) + (4x + 5)

• 9x -7

• -9x-11

• 9x+7

• x+7

Multiple Choice

Find the sum.

(3 - 2x + 2x²) + (4x - 5 + 3x²)

• 7x - 7x + 5x²

• 5x² + 2x - 2

• 5x²

• 5x² + 6x + 8

Multiple Choice

Add to Simplify:
 (4x - 2x³) + (5x³ - 4x + 5)

• 3x³ + 5
• 3x³ + 8x + 5
• 3x² + 5
• 7x³ + 8x + 5

Multiple Choice

Add or Subtract to Simplify:
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

• 4b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 4
• b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 7

Multiple Choice

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x
• 7x⁵ - 6x
• -5x³ + 2x² - 6x
• -5x⁵ - 6x

Multiple Choice

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2 
• x + 2
• 2x² + x - 10 
• x - 10 

Multiple Choice

Add or Subtract to Simplify:
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3 
• -7n² - 8n + 3 
• -6n² - 8n + 3
• -7n² - 4n + 3

Multiple Choice

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

• 3x² - x
• 4x² + 2x
• 3x² + 3x
• 3x² + 2x

Open Ended

Multiple Choice

Simplify each Expression:
(7p + 4p³ - 8) - (-3p² + 2 - 9p)

• -3p² + 4p³ -15 + 9
• 3p³ + 4p² - p + 3
• 4p³ +3p² +16p -10
• 4p³ +3p² + 16p + 10

Multiple Choice

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

• 4b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 4
• b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 7

Multiple Choice

Find the difference. 
(3- 2x + 2x²) - (4x -5 +3x²)

• x_² + 6x + 8
• 2x² + 5x - 7
• -x² -6x + 8
• -2x² + 11x - 4

Multiple Choice

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x
• 7x⁵ - 6x
• -5x³ + 2x² - 6x
• -5x⁵ - 6x

Multiple Choice

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x
• 7x⁵ - 6x
• -5x³ + 2x² - 6x
• -5x⁵ - 6x

Multiple Choice

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2 
• x + 2
• 2x² + x - 10 
• x - 10 

Multiple Choice

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

• 3x² - x
• 4x² + 2x
• 3x² + 3x
• 3x² + 2x

Multiple Choice

What is the perimeter of the rectangle?

• x²+8x-5

• 2x²+16x-10

• 2x²+10x-8

• 6x-2

Multiple Choice

(3x²+xy-5y²) +
(2x²-xy+3y²)

• 5x²-2xy+8y²
• 5x²-2y²
• 5x²+2y²
• 5x²+2xy-8y²

Multiple Choice

Combine like terms to simplify:
 (5x + 2) + (4x + 5)

• 9x -7
• -9x-11
• 9x+7
• x+7

Multiple Choice

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

• 11a³ - 4a² - 14a - 7 
• 5a³ - 4a² - 14a - 7 
• 5a³ - 4a² - 20a - 7 
• 5a³ - 9a² - 20a - 7