Types of Factoring Polynomials

Factoring Different Types of Polynomial

Quarter 1Week 1 Module 1a

Multiple Choice

What is the Greatest Common Factor of 24 and 54?

• 1

• 2

• 3

• 6

Multiple Choice

What is the GCF of 20, 24, and 40?

• 1

• 4

• 8

• 20

Multiple Choice

What is the GCF of  $$x^2$$   and $$x^9$$  ?

• $$x^2$$   

• $$x^7$$  

• $$x^{11}$$  

• $$x^{18}$$  

Multiple Choice

What is the GCF of $$xy^{10}$$  , $$x^4y^6$$   ,  $$x^9y^9$$  , and $$x^{10}y^{10}$$  ?

• $$xy$$  

• $$xy^6$$  

• $$x^4y^4$$  

• $$x^4y^6$$  

Multiple Choice

Factor using GCF or monomial factoring:

2n²-8n³

• 2n²(n-4n²)

• 2n²(1-4n)

• 2n³(10-8n²)

• 3n(1-4n)

Multiple Choice

Factor out the GCF:

10x³ - 15x

• x(10x² - 15)

• 5x(2x² - 3)

• 5(2x³ - 3x)

• 5x²(10x - 3)

Multiple Choice

Which of the following is a perfect square expression?

• $$3x^2$$

• $$4x$$

• $$9x^3$$

• $$16x^4$$

Multiple Choice

If one factor of the difference of two squares is x + 2, what is the other factor?

• $$x-2$$

• $$x^2-2$$

• $$x^2-2^2$$

• $$\left(x^{ }-2\right)^2$$

Multiple Choice

If one factor of the difference of two squares is x + 2, what is the other factor?

• $$x-2$$

• $$x^2-2$$

• $$x^2-2^2$$

• $$\left(x^{ }-2\right)^2$$

Multiple Choice

What is the complete factored form of $$z^2-16$$  ? 

• $$\left(z-4\right)^2$$  

• $$\left(z-8\right)^2$$  

• $$\left(z-4\right)\left(z-4\right)$$  

• $$\left(z+4\right)\left(z-4\right)$$  

Multiple Choice

What is the complete factored form of the expression $$y^4-49$$  ?

• $$(𝑦^2)^2−(7^2)^2$$  

• $$\left(y^2-7\right)^2$$  

• $$\left(y^2+7\right)^2$$  

• $$\left(y^2-7\right)\left(y^2+7\right)$$  

Multiple Choice

Which of the following polynomials has factors (𝑥𝑦 – 1)(𝑥𝑦 + 1)?

• $$x^2y-1$$

• $$x^2y^2-1$$

• $$xy^2-1$$

• $$x^2y^2+1$$

Multiple Choice

Which of the following expressions is a perfect cube?

• $$8x$$

• $$27x^2$$

• $$64x^6$$

• $$125x^4$$

Multiple Choice

Which of the following is the complete factored form of the cubic polynomial  $$x^3-8$$   ?

• $$(𝑥−2)(𝑥^2+2𝑥+4)$$  

• $$(𝑥+2)(x^2−2𝑥+4)$$  

• $$(𝑥−2)(𝑥^2+2𝑥−4)$$  

• $$(𝑥−2)(𝑥^2−2𝑥+4)$$  

Multiple Choice

$$Factor\ completely:\ 27𝑥^3+64𝑦^3$$  

• $$(3𝑥)^3+(4𝑦)^3$$  

• $$(3𝑥+4𝑦)(9𝑥^2−12𝑥𝑦+16𝑦^2)$$  

• $$(3𝑥+4𝑦)(3𝑥^2−3𝑥𝑦+16𝑦^2)$$  

• $$(3𝑥+4𝑦)(3𝑥^2−12𝑥𝑦+4𝑦^2)$$  

Multiple Choice

Your classmate was asked to square (2𝑥 – 3), he answered  $$4x^2-9$$   . Is his answer correct? 

• Yes, because product rule is correctly applied.

• Yes, because squaring a binomial always produces a binomial product.

• No, because the answer must be $$4x^2+9$$  .

• No, because squaring a binomial always produces a trinomial product.