Polynomials

Polynomial Vocab

100

What is the degree of the polynomial 2x⁵ + 3x?

A. 1

B. 2

C. 5

D. 6

C. 5

The degree is the highest exponent in the polynomial.

2x⁵ + 3x

200

What is the coefficient in the term 4x²?

A. 4

B. x

C. 2

D. Negative

Answer:  The coefficient in the term 4x² is 4.

300

5x³ and _____ are "like terms".

A. 5x

B. 5

C. 2x³

D. 2x⁴

5x³ and 2x³ are "like terms".  (They have the same variable and exponent.)

400

Which polynomial is in Standard Form?

A. 2x + x² + 5x³

B. 5x³ + x² + 2x

C. 10 + 8x

D. (x + 5)(2x - 6)

B. 5x³ + x² + 2x   The exponents are in decreasing order.

500

y = 3(x - 5) and ____ are equivalent functions.

A. y = 15

B. x = 1

C. y = 3 - 15

D. y = 3x - 15

y = 3(x - 5) and y = 3x - 15 are equivalent functions.

Equivalent functions have the same result for any value of x.

Adding Polynomials

100

Which of following is false?

A. 2x + 3x = 5x

B. 10x² - x² = 9x² 

C. 7x + x²​​​​ = 8x²

D. -2x² + 2x² = 0

C. 7x + x² = 8x² is false.  You cannot add 7x and 8x² because they have different exponents.

200

 x² + 3x + 3x + 9 =

A. x² + 6x + 9

B. 16

C. 16x² 

D. x² + 15

A. x² + 3x + 3x + 9 = x² + 6x + 9

300

What is -3x² + 4x + 1 + 4x² ?

A. 7x² + 4x + 1

B. -7x² + 4x + 1

C. x² + 4x + 1

D. -x² + 4x + 1

C. -3x² + 4x + 1 + 4x² =

x² + 4x + 1

400

Polynomial A = 2x² + 6x - 10.  

Polynomial B = -3x + 10.  The sum of A + B is

A. A trinomial with a leading coefficient of -1

B. A binomial with degree 2

C. A monomial with a leading coefficient of 5

D. A binomial with a degree of 1.

B. A binomial with degree 2

Polynomial A = 2x² + 6x - 10.  

Polynomial B = -3x + 10.  The sum of A + B

500

If x = 3, what is the value of x² + 2x + 1 + (3x - 11)?

A. 7x

B. 14

C. 11

D. 34

B. 14:  Because  x² + 2x + 1 + (3x - 11)

                      = x² + 5x - 10

                       = 3² + 5(3) - 10

                        = 9 + 15 - 10

                        = 14

Subtracting polynomials

100

What is 3x - 2x?

A. 1

B. x

C. -1

D. -x

B. 3x - 2x = x

200

2x² + 5x - 3 - (x² + 2x - 10) is the same as

A. 2x² + 5x - 3 - x² -2x + 10

B. 2x² + 5x - 3 - x² + 2x - 10

A. 2x² + 5x - 3 - (x² + 2x - 10) is the same as

2x² + 5x - 3 - x² -2x + 10

300

What is x² - 6 - (2x + 8)?

A. x² - 2x + 2

B. -x² - 14

C. x² - 2x - 14

D. 3x² + 2

x² - 6 - (2x + 8) = x² - 2x - 14

(C)

400

What is x² + 2x minus x² + 5?

A. 2x + 5

B. 2x- 5

C. -2x + 5

D. -2x - 5

x² + 2x minus x² + 5 = 

x² + 2x - (x² + 5)

x² + 2x - x² - 5

 2x - 5        (B)

500

If x = 10, What is 5x² - 2x²?

A. 30

B. 60

C. 300

D. 10

5x² - 2x² = 3x²

              = 3(10)²

              = 3(10)(10) 

              = 300          D

Multiplying Polynomials

100

What is x² times x³ ?

A. x⁶

B. 2x²

C. 2x³

D. x⁵

x² (x³) = x⁵

200

What is 3x² times 4x³?

A. 7x⁵

B. 7x⁶

C. 12x⁵

D. 12x⁶

C. 3x² times 4x³ = 12x⁵

300

2x(x² + 6x - 10) = 

A. 2x³ + 12x² - 20x

B. 2x² + 12x - 20

C. -6x

D.  2x³ + 12x² + 20x

2x(x² + 6x - 10) = 

A. 2x³ + 12x² - 20x

400

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

A. 10x² - 8x - 12

B. 10x² + 23x - 12

C. 10x² + 7x - 12

D.  10x² - 7x + 12

C.     (2x + 3)(5x - 4) =

       10x² + -8x + 15x - 12

       = 10x² + 7x - 12

500

Which of the following is equivalent to x² - 25?

A. (x - 5)²

B. 5(x - 5)

C. (x + 5)(x + 5)

D. (x + 5)(x - 5)

D.  x² - 25 = 

                    (x + 5)(x - 5)

Evidence:       x² - 5x + 5x - 25

                   = x²     + 0 -    25