Divide Polynomials by Monomials

Polynomials

Vocabulary, Classifications, and Operations

Polynomials Vocabulary

● Variable (a letter) - represents a quantity that can

vary or change

● Constant (not changing fixed) - a number or symbol

for a non-changing value (6, 234, 𝜋 ) that is NOT
next to a letter (not being multiplied by a variable)

● Coefficient - a number or value NEXT TO A

LETTER or variable that acts as a multiplier
(including the invisible 1)

Polynomials Vocabulary

● Monomial - a number, a variable, or the product

of a number and one or more variables (1 term)

● Binomial - polynomial with 2 terms
● Trinomial - polynomial with 3 terms
● Polynomial - a monomial or the sum of

monomials (4 terms or more)

In your notebook, write the expression below and label it
(like in the examples above) with these vocabulary words:
Constant, Variable, Coefficient, Exponent, Base, Term.

Multiple Choice

Classify the following polynomial

• quartic polynomial

• quadratic polynomial

• quartic trinomial

• quadratic trinomial

Multiple Choice

Classify the following polynomial

• quadratic trinomial
• cubic binomial

Multiple Choice

Classify the polynomial:
3x² – 8x + 1

• quadratic trinomial

• cubic trinomial

• quadratic binomial

• cubic binomial 

Multiple Choice

Is this expression in Standard Form?
6w² - 9w³

• Yes

• No

Multiple Choice

What is the degree?
 - 3x³ - x² - 10x + 12

• 1

• 2

• 3

• 4

Multiple Choice

Find the GCF.

$$12c^2-20a^2$$  

• $$2$$

• $$4$$

• $$2a^2c^2$$  

• $$4ac$$  

• The GCF is 1 because the polynomial is prime.

Multiple Choice

$$\frac{\left(5x^2-15y^3\right)}{5}$$  

• $$x^2-3y^3$$  

• $$x^2-15y^3$$  

• $$10x^2-20y^3$$  

• $$5x^2-3y^3$$  

Multiple Choice

Which choice shows the GCF of 18k and 15k³ ?

• 3k²

• 3k³

• 3k

• 5k

• 1, because the polynomial is prime

Multiple Choice

$$\frac{\left(m^2n+m^6n^3\right)}{mn}$$  

• $$m^3n^2+m^7n^4$$  

• $$m^2n+m^5n^2$$  

• $$m+m^5n^2$$  

• $$m+m^6n^3$$  

Multiple Choice

Find the greatest common factor.

$$64-40ab$$  

•  4

• 4ab 

•  8ab

• 8 

• 2

Multiple Choice

$$\left(14d^3-21d^8\right)\div\ 7d^2$$  

• $$7d-21d^6$$  

• $$7d^{1.5}-14d^4$$  

• $$2d-3d^6$$  

• $$2d^{1.5}-3d^4$$  

Multiple Choice

Determine the greatest common factor.

$$36a^2+24a$$  

• 12a 

•  6a

• 12a² 

• 4a 

• 8a

Multiple Choice

$$\frac{\left(8x^4+6x^3-10x^2\right)}{2x^2}$$  

• $$4x^2+3x-5$$  

• $$4x^2+3x^{1.5}-5x$$  

• $$6x^2+4x-12$$  

• $$6x^2+4x^{1.5}-12x$$  

Multiple Choice

Find the GCF.

$$18x^4-12x^2$$  

• 6x² 

• 2x² 

• 6x 

• 6x⁴ 

• 2x⁴

Multiple Choice

$$\frac{\left(15mn^2+30m^3n^4+45n^5\right)}{5}$$  

• $$10mn^2+25m^3n^4+40n^5$$  

• $$20mn^2+35m^3n^4+54n^5$$  

• $$15mn^2+6m^3n^4+45n^5$$  

• $$3mn^2+6m^3n^4+9n^5$$  

Multiple Choice

Find the greatest common factor.

$$14x-21x^2$$  

• 7x²

• 4x 

• That is a prime polynomial, so the GCF is 1.

• 7x 

• 2x²

Multiple Choice

$$\frac{\left(-18x^5-12x^3-6x^2\right)}{-3x}$$  

• $$-15x^4-9x^2-3x$$  

• $$-6x^4-4x^2-2x$$  

• $$6x^4+4x^2+2x$$  

• $$6x^5+4x^3+2x^2$$  

Multiple Choice

Which choice is the GCF?

$$81m+48mn$$  

•  3m

• It's Prime.

  (The GCF is 1.) 

• 6 

• mn 

• 9m

Multiple Choice

What is $$10h^4k^2+20h^3k^3+30h^2k^4$$  divided by  $$10hk$$  ?

• $$20h^5k^3+30h^4k^4+40h^3k^5$$  

• $$h^3k+2h^2k^2+3hk^3$$  

• $$h^4k^2+2h^3k^3+3h^2k^4$$  

• $$0h^3k+10h^2k^2+20hk^3$$  

Multiple Choice

Determine the GCF.

$$36ab^2-48a^2b$$  

• a²b²

• 6ab 

• 12a²b² 

• 12ab 

• 8ab

Multiple Choice

$$\frac{\left(x^6y^8-x^4y^6+x^2y^4\right)}{x^2y^2}$$  

• $$x^4y^6-x^2y^4+y^2$$  

• $$x^3y^4-x^2y^3+xy^2$$  

• $$x^8y^{10}-x^6y^8+x^4y^6$$  

• $$0x^4y^6-0x^2y^4+0y^2$$  

Multiple Choice

Find the greatest common factor.

$$x^3y^2+x^2y+x$$  

• xy 

• x 

• y 

• x³y² 

• It's Prime.

  (The GCF is 1.)

Multiple Choice

$$\frac{20x^2}{5x}$$  

• $$15x$$  

• $$4x$$  

• $$15x^2$$  

• $$25x$$  

Multiple Choice

Which choice is the GCF?

$$8m^2n^2-24mn^3+16mn$$  

• 4mn 

•  8mn

• 6mn 

• mn 

• 2mn

Multiple Choice

$$\frac{36m^2n^5}{9m^2n^3}$$  

• $$27n^2$$  

• $$4mn^2$$  

• $$45m^4n^8$$  

• $$4n^2$$  

Multiple Choice

Find the GCF of the trinomial.

$$9xz^3+18yz^2+24z^2$$

• 3z² 

• 6z² 

• 3xyz 

• 3z 

• 3z³

Multiple Choice

Simplify this expression.

• 5p² - 16p
• 5p + 4
• 5p - 4
• 5p + 4p

Multiple Choice

Find the GCF.

w³ + 3w

• 3w

• w

• w³

• 3

• 3w³

Multiple Choice

Simplify this expression.

• -5x¹⁰
• 4x⁴ + 18x⁶
• -6x⁴ + 16x²
• 4x⁴ - 9x²

Multiple Choice

What is the GCF?

2x²-4x+8

• 2x

• 2

• x

• 1

• 8

Multiple Choice

Divide (6x²+12x) by 3x

• 2x+4
• 2+6/3x
• 2+4/x
• 3+6/2x

Multiple Choice

Which choice is the GCF?

5x²+20x

• 5

• x

• 5x

• 20x

• 2x

Multiple Choice

Divide the polynomial by the monomial.

• 2x⁸-8x²-28x
• 2x⁸-2x²-7x
• 8x⁷-8x-28x
• 2x⁷ -2x -7

Multiple Choice

Determine the greatest common factor.

$$25x^2+4y$$  

• 5x

• 4

• xy

• 2xy

• The GCF is 1 because the polynomial is prime.

Multiple Choice

Divide the polynomial by the monomial.

• 15x⁹ - 8x³
• 3x⁶ - 8x³
• -5x¹²
• 3x⁶ - 40x³

Multiple Choice

Divide the polynomial by the monomial.

• 15x⁹ - 8x³
• 3x⁶ - 8x³
• -5x¹²
• 3x⁶ - 40x³

Multiple Choice

Divide 8x² -4x + 12  by 2x

• 4x+2
• 4x-2+6/x
• 4x-2
• 4x-2+1/(6x)

Multiple Choice

Divide:
(9x² + 6x)  ÷ 3x

• 3x + 2
• 3x² + 2x
• 5x²
• 3x + 6

Multiple Choice

• 5w ² − 4w + 3
• 12w ² − 9w + 6
• 12w ² − 12w + 9
• 5w ² − 12w+ 9

Multiple Choice

Divide the polynomial by the monomial.

• 2x⁸-8x²-28x
• 2x⁸-2x²-7x
• 8x⁷-8x-28x
• 2x⁷ -2x -7