Factoring Completely

Primes Of Polynomials

By KATIE KENNEDY

Multiple Select

Which of the polynomials can be factored using difference of squares?

(Select all that apply)

• $$36x-25x^9$$

• $$x^6-z^4$$

• $$4x^2+81$$

• $$x^2-22x+121$$

• $$x^9-y^{15}$$

Multiple Select

Which of the polynomials can be factored using difference of cubes?

(Select all that apply)

• $$216-125x^9$$

• $$x^6-27x^4$$

• $$4x^2+81$$

• $$x^2-22x+121$$

• $$x^9-y^{15}$$

Multiple Select

Which of the polynomials can be factored using sum of cubes?

(Select all that apply)

• $$125x^3+64y^9$$

• $$x^6-x^3$$

• $$8x^3+27$$

• $$x^3+20x+1000$$

• $$x^9-x^{15}$$

Multiple Select

Which of the polynomials is a perfect square trinomial?

(Select all that apply)

• $$64-48x+9x^2$$

• $$x^6-x^{12}$$

• $$4x^2+7x-81$$

• $$x^2+20x+100$$

• $$100x^4-99x^2+25$$

Multiple Choice

Which special factoring form is not used in prime factoring of polynomials?

• $$DOS$$

• $$DOC$$

• $$PST$$

• $$SOS$$

• $$SOC$$

Math Response

What is the correct factored form for $$27x^3-363xy^2$$

Type answer here

Correct Answer: 3x\left(3x+11y\right)\left(3x-11y\right)

Deg^°

Rad

Math Response

What is the correct factored form for $$18x^2-72x+72$$

Type answer here

Correct Answer: 18\left(x-2\right)^2

Deg^°

Rad

Math Response

What is the correct factored form for $$x^3-x^2-4x+4$$

Type answer here

Correct Answer: \left(x+2\right)\left(x-2\right)\left(x-1\right)

Deg^°

Rad

Math Response

What is the correct factored form for $$yz^2-y^3+z^3-y^2z$$

Type answer here

Correct Answer: \left(z+y\right)^2\left(z-y\right)

Deg^°

Rad

Math Response

What is the correct factored form for $$2wx^2+x^2z-2wy^2-y^2z$$

Type answer here

Correct Answer: \left(2w+z\right)\left(x+y\right)\left(x-y\right)

Deg^°

Rad

Math Response

What is the correct factored form for $$x^2a+x^2b-16a-16b$$

Type answer here

Correct Answer: \left(a+b\right)\left(x+4\right)\left(x-4\right)

Deg^°

Rad

Math Response

What is the correct factored form for $$3x^5+192x^2$$

Type answer here

Correct Answer: 3x^2\left(x+4\right)\left(x^2-4x+16\right)

Deg^°

Rad

Categorize

Options (10)

$$\left(x^2+y^2\right)$$  

$$\left(3x+7y\right)$$  

$$\left(x^2-y^2\right)$$  

$$\left(x^2-9x+25\right)$$  

$$\left(2x-8\right)$$  

$$\left(x^2-10x+25\right)$$  

$$\left(7x^2-25xy+14y\right)$$  

$$\left(x^3+343\right)$$  

$$\left(\frac{1}{4}x^3+\frac{2}{3}\right)$$  

$$\left(6xy-16y\right)$$  

Sort the factors into the correct category:

Prime

Not prime

Categorize

Options (8)

$$\left(x+4\right)\left(x-4\right)$$  

$$\left(b+4\right)\left(a-5\right)^2\left(b-4\right)$$  

$$\left(b+4\right)\left(a-5\right)^2\left(b^2-4\right)$$  

$$\left(x-5\right)\left(x^2+5x+25\right)$$  

$$\left(x-4\right)\left(2x-8\right)$$  

$$\left(x-5\right)\left(x^2-10x+25\right)$$  

$$\left(x-5\right)\left(x^2+25\right)$$  

$$\left(x+5\right)\left(x^2-25\right)$$  

Sort the polynomials into the correct category:

Factored Completely

Not factored completely

Drag and Drop

Determine the polynomial that matches how we will factor

Diamond Factoring ​

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DOS​

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PST​

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Texas Factoring​

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Factor By Grouping​

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Drag these tiles and drop them in the correct blank above