Algebra 1: Polynomials (PART 1)

Classify Polynomials

100

Classify the polynomial by its degree and number of terms. 

5x³

Cubic Monomial

200

Classify the polynomial by its degree and number of terms. 

2x + 6

Linear Binomial

300

Classify the polynomial by its degree and number of terms. 

4x² + 4x - 6

Quadratic Trinomial

400

Classify the polynomial by its degree and number of terms. 

-2x⁵ + 3x² - 3x + 2

Quintic Polynomial with 4 terms

500

Classify the polynomial by its degree and number of terms. 

5x⁹ + 2x³ - 3x² - 4x + 1

9th degree Polynomial with 5 terms

Add and Subtract Polynomials

100

Simplify. Write you answer in standard form.

(12y² + 17y - 4) + (9y² - 13y + 3)

21y² + 4y - 1

200

Simplify. Write you answer in standard form.

(3x² - x) - (x² + 3x + 5)

2x² - 4x - 5

300

Simplify. Write you answer in standard form.

(-3m² + m³) + (4m² + 6m)

m³ + m² + 6m

400

Simplify. Write you answer in standard form.

(6x³ - 4x² + x - 9) - (3x² + 7x + 3)

6x³ - 7x² - 6x - 12

500

Simplify. Write you answer in standard form.

-(3 + 4z) - (6z² - 2)

-6z² - 4z - 1

Multiply Polynomials

100

Multiply. Write you answer in standard form.

-3a(5a² + 2a) 

-15a³ - 6a²

200

Multiply. Write you answer in standard form.

(x + 6)(x - 3)

x² + 3x - 18

300

Multiply. Write you answer in standard form.

(3y + 2)(y - 4) 

3y² - 10y - 8

400

Multiply. Write you answer in standard form.

(x - 3)²

x² - 6x + 9

500

Multiply. Write you answer in standard form.

(2x + 3)(x² - 4x - 7)

2x³ - 5x² - 26x - 21

Factor Polynomials

100

Factor using the GCF.

9x - 36

9(x - 4)

200

Factor using the GCF.

−3k³ + 15k² − 6k

3k(−k² + 5k − 2)

300

Factor by grouping.

m³ − m² + 2m − 2

(m² + 2)(m − 1)

400

Factor by grouping.

12a³ − 9a² + 4a − 3

(3a² + 1)(4a − 3)

500

Factor by grouping.

40xy + 30x − 100y − 75

5(2x − 5)(4y + 3)

RANDOM

100

50 pts. Write the polynomial in standard form:

-3x + 5x³ - x⁵ + 8x²

50 pts. Identify the leading coefficient.

-x⁵ + 5x³ + 8x² - 3x

Leading Coefficient = -1

200

Simplify. Write your answer in standard form. 

6 - 2x(3x - 2) - x 

-6x² + 3x + 6

300

Multiply. Write you answer in standard form.

(x + 8)²

x² + 16x + 64

400

Simplify. Write your answer in standard form. 

(-3y² - 4y - 8) - (-3y² + 3y) - 7y - 3

-14y - 11

500

Multiply. Write you answer in standard form.

(3x²y + 2y)(3xy + 2y + 3x +1)

9x³y² + 6x²y² + 9x³y + 3x²y + 6xy² + 4y² + 6xy + 2y

Identify the Error

100

Question: Find the GCF of 30 and 75. 

Answer: GCF is 5. 

Explain the mistake and state the correct answer.

They didn't take out the GREATEST common factor.

Correct Answer: The GCF is 15.

200

Question: Factor completely using grouping:

15x^3-10x^4+8x-12

Answer:  5x^3(3-2x)+4(2x-3) 

Explain the mistake and state the correct answer.

They did not finish the problem AND they did not write the polynomial in standard form before using grouping. 

Correct Answer: 

(2x-3)(-5x^3+4)

300

Question: Classify the polynomial by the degree and number of terms. 

 -2x^2+5x^3-13+x 

Answer: Quartic (4th degree) Binomial (2 terms)

Explain the mistake and state the correct answer.

They did not write the polynomial in standard form first AND mixed up the words for the degree and number of terms. 

Correct Answer: Cubic (3rd degree) Polynomial with 4 Terms.

400

Question: Add/subtract the polynomials.

  (-3m^2+m^3)+(4m^2+6m) 

Answer:  4m^6-12m^4+6m^3-18m^2 

Explain the mistake and state the correct answer.

They multiplied the polynomials instead of adding.

Correct Answer: 

m^3+m^2+6m

500

Question: Multiply. 

 6pr(2p-r) 

Answer: 

6p^2r

Explain the mistake and state the correct answer.

They tried to combine like terms after distributing but these are not like terms.

Correct Answer: 

12p^2r-6pr^2