Dividing Polynomials by Monomials

quartic polynomial

quadratic polynomial

quartic trinomial

quadratic trinomial

quadratic trinomial

cubic trinomial

quadratic binomial

cubic binomial 

Yes

No

1

2

3

4

$$2$$

$$4$$

$$2a^2c^2$$  

$$4ac$$  

The GCF is 1 because the polynomial is prime.

$$x^2-3y^3$$  

$$x^2-15y^3$$  

$$10x^2-20y^3$$  

$$5x^2-3y^3$$  

3k²

3k³

3k

5k

1, because the polynomial is prime

$$m^3n^2+m^7n^4$$  

$$m^2n+m^5n^2$$  

$$m+m^5n^2$$  

$$m+m^6n^3$$  

 4

4ab 

 8ab

8 

2

$$7d-21d^6$$  

$$7d^{1.5}-14d^4$$  

$$2d-3d^6$$  

$$2d^{1.5}-3d^4$$  

12a 

 6a

12a² 

4a 

8a

$$4x^2+3x-5$$  

$$4x^2+3x^{1.5}-5x$$  

$$6x^2+4x-12$$  

$$6x^2+4x^{1.5}-12x$$  

6x² 

2x² 

6x 

6x⁴ 

2x⁴

$$10mn^2+25m^3n^4+40n^5$$  

$$20mn^2+35m^3n^4+54n^5$$  

$$15mn^2+6m^3n^4+45n^5$$  

$$3mn^2+6m^3n^4+9n^5$$  

7x²

4x 

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

7x 

2x²

$$-15x^4-9x^2-3x$$  

$$-6x^4-4x^2-2x$$  

$$6x^4+4x^2+2x$$  

$$6x^5+4x^3+2x^2$$  

 3m

It's Prime.

(The GCF is 1.) 

6 

mn 

9m

$$20h^5k^3+30h^4k^4+40h^3k^5$$  

$$h^3k+2h^2k^2+3hk^3$$  

$$h^4k^2+2h^3k^3+3h^2k^4$$  

$$0h^3k+10h^2k^2+20hk^3$$  

a²b²

6ab 

12a²b² 

12ab 

8ab

$$x^4y^6-x^2y^4+y^2$$  

$$x^3y^4-x^2y^3+xy^2$$  

$$x^8y^{10}-x^6y^8+x^4y^6$$  

$$0x^4y^6-0x^2y^4+0y^2$$  

xy 

x 

y 

x³y² 

It's Prime.

(The GCF is 1.)

$$15x$$  

$$4x$$  

$$15x^2$$  

$$25x$$  

4mn 

 8mn

6mn 

mn 

2mn

$$27n^2$$  

$$4mn^2$$  

$$45m^4n^8$$  

$$4n^2$$  

3z² 

6z² 

3xyz 

3z 

3z³

3w

w

w³

3

3w³

2x

2

x

1

8

5

x

5x

20x

2x

5x

4

xy

2xy

The GCF is 1 because the polynomial is prime.