Monomial Lesson

First_Review_Grade 8

by Fely Cayetano

​Greatest Common Factor

​- refers to the common factor having the greatest numerical factor and with variables having the least degree.

Multiple Choice

Find the GCF of each pair of monomials.

$$6a\ and\ 18ab$$  

• 3a

• 6a

• 9a

• 6ab

Multiple Choice

Find the GCF of each pair of monomials.

$$10a\ and\ 12a^2b$$  

• 2ab

• 4a

• $$2a^2b$$  

• 2a

Multiple Choice

Find the GCF of each pair of monomials.

$$8ab^3\ and\ 10a^2b^2$$  

• 2ab

• $$2ab^2$$  

• $$2a^2b$$  

• 2a

​Factoring a Polynomial

​- rewriting a polynomial as a product of polynomials of smaller degree

​Common Monomial Factor

Multiple Choice

Factor using GCF or monomial factoring:

2n²-8n³

• 2n²(n-4n²)

• 2n³(10-8n²)

• 2n²(1-4n)

• 3n(1-4n)

Multiple Choice

Factor out the GCF: 10x³ - 15x

• x(10x² - 15)

• 5(2x³ - 3x)

• 5x(2x² - 3)

• 5x²(10x - 3)

Multiple Choice

Factor out the GCF: $$16x^3y-32x^2y^2+24xy^3-16xy$$

• $$8x(2x^2y-4xy^2+3y^3-2y)$$  

• $$8y(2x^3-4x^2y+3xy^2-2x)$$  

• $$8xy(2x^2-4xy+3y^2-2)$$  

​Factoring by grouping

Multiple Choice

Factor: x² + 8x + 2x + 16

• (x+2)(x+8)

• (x+1)(x+16)

• (x-2)(x-8)

• (x+6)(x+10)

Multiple Choice

Factor: 4p³ + 8p² + 3p + 6

• (2p²+3)(p+2)

• (4p²+3)(p+2)

• (2p²+6)(p+4)

• (4p²+8p)(3p+6)

​Factoring the Difference of Two Squares

Multiple Choice

Factor x² – 16.

• (x + 2)(x – 8)

• (x + 4)(x + 4)

• (x – 4)(x – 4)

• (x + 4)(x – 4)

Multiple Choice

Factor the Following: 25x²-81

• (5x-9)²

• 25(x-9)²

• (5x+9)(5x-9)

• (9x+5)(9x-5)

Multiple Choice

Factor: x² - 30x + 225

• (x + 15)²

• (x + 25)²

• (x - 15)²

• (x - 25)²

Multiple Choice

Factor: n² + 10n + 25

• (n + 5)(n - 5)

• (n - 5)²

• (n + 25)(n + 1)

• (n + 5)²

Multiple Choice

Factor: 64x³ + 1

• (4x - 3)(16x² + 12x + 9)

• (2x - 1)(4x² + 2x + 1)

• (3x - 1)(9x² + 3x + 1)

• (4x + 1)(16x² - 4x + 1)

Multiple Choice

Which of the following is the complete factored form of:

$$x^3y^9+1000$$  

• $$(xy^3+10)(x^2y^6−10xy^3+100)$$

• $$(xy^3−10)(x^2y^6+10xy^3+100)$$

• $$(xy+10)(x^2y^2−10xy+100)$$

• $$(xy^3−10)(x^2y^3−20xy^3+100)$$

Multiple Choice

Factor :   $$27x^3−64$$  

• $$(3x+4)(9x^2−12x+16)$$  

• $$(3x−4)(9x^2−12x+16)$$  

• $$(3x+4)(9x^2+12x+16)$$  

• $$(3x−4)(9x^2+12x+16)$$  

Multiple Choice

Factor :   $$64x^6−y^6$$  

• $$(4x^2+y^2)(16x^4−4x^2y^2-y^4)$$  

• $$(4x^2+y^2)(16x^4−4x^2y^2+y^4)$$  

• $$(4x^2-y^2)(16x^4−4x^2y^2-y^4)$$  

• $$(4x^2-y^2)(16x^4+4x^2y^2+y^4)$$