Factor Review Ch 6 Honors Alg 1

GCF Factoring

Finding the GCF

• Find the largest number that divides evenly into all of the terms coefficients

• If all of the terms share the same variable(s) use those with the smallest exponent

Multiple Choice

What is the GCF of 18k and 15k³

• 3k²
• 3k³
• 3k
• 5k

Multiple Choice

What is the GCF of

$$24xy^2,\ 36x^3y^5z,\ and\ 18x^2y^3z^2$$  

• $$6xy^2$$  
  

• $$6x^3y^5z^2$$  
  

• $$12xyz$$  
  

• $$12xy^2$$  
  

Factoring a polynomial means expressing it as a product of other polynomials.

• Find the greatest common factor     (GCF).

• Divide the polynomial by the GCF. The quotient is the other factor.

• Express the polynomial as the product of the quotient and the GCF.

Multiple Choice

Factor:
56a³-8a

• 8a²(56a³-8a)
• 8a(7a²-1)
• 8a(7a³-a)
• 8a²(35a²-a)

Multiple Choice

Factor:
 2n²-8n³

• 2n²(n-4n²)
• 2n²(1-4n)
• 2n³(10-8n²)
• 3n(1-4n)

Multiple Choice

Factor 4x - 20

• 4(x -5)
• 4(x + 5)
• 4x(1 - 5)
• 4x(1 + 5)

Multiple Choice

Factor:
p² - 14p

• p(1 - 14)
• 2p(p - 7)
• p²(1-14)
• p(p - 14)

Multiple Choice

Factor Completely:
2x² - 2x - 6

• 2(x + 3)(x - 1)
• 2(x + 2)(x - 3)
• 2(x² - x - 3)
• 2(x² - 2x - 6)

Multiple Choice

Factor by GCF:
17xy - x

• 17(xy - x)
• y(17x - x)
• x(17y - 1)
• not factorable

Multiple Choice

Factor by GCF:
6m² + 16m

• 2(3m² + 8m)
• 2m(3m + 8)
• 2m(3m - 8m)
• not factorable

Multiple Choice

4.) Factor

x² - 25

• ( x + 5 ) ( x - 5 )

• ( x - 5 ) ( x - 5 )

• ( x + 5 ) ( x + 5 )

• Prime

Multiple Choice

3.) Factor the Difference of Squares:

81m² - 1

• not factorable

• (m-9)(m+9)

• 9m(9m-1)

• (9m-1)(9m+1)

Multiple Choice

What is the first question you ask yourself when factoring a polynomial? 

• How many terms does it have? 
• Is there a GCF? 
• What strategy should I use? 
• Why do I have to learn this?!?!?!

Multiple Choice

Factor Completely:
4x² + 64

• 4(x² + 16)
• 4(x - 4)(x + 4)
• 4(x² + 64)
• Prime

Multiple Choice

Factor 25x² - 81.

• (5x -  9)(5x + 9)
• (5x - 9)(5x - 9)
• (5x + 9)(5x + 9)
• cannot be factored

Factor by grouping

Factoring by grouping works with four-term polynomials of higher degree.

Look to see if you can factor out a GCF first, and double check that your factors aren't perfect squares that need to be factored again. 

Split it in half
Take out the GCF from each half
The ( ) should match

Multiple Choice

x³-5x²+5x-25

• (x²-5)(x-5)
• (x²+5)(x-5)
• (x²+5)(x+5)
• (x²-1)(x-25)

Multiple Choice

30x³+15x²-18x-9

• (5x²-3)(6x+1)
• (5x²-3)(6x+3)
• 3(5x²+3)(2x-1)
• 3(5x²-3)(2x+1)

Factoring Completely

1) Is there a GCF?

2) How many terms are left to be factored?

3) If it is a trinomial, can it be factored using the X method?

4) If it is a binomial, is it a difference of squares? A sum of cubes? A difference of cubes?

Multiple Choice

Factor the polynomial completely. Which is the completely factored polynomial?

$$4x^3-12x^2+7x-21$$  

• $$4x^2\left(x+4\right)$$  

• $$3x^2\left(x-3\right)$$  

• $$\left(4x^2-7\right)\left(x+3\right)$$  

• $$\left(4x^2+7\right)\left(x-3\right)$$  

Multiple Choice

Completely factor the polynomial:

$$8x^2-24x+20x-60$$  

• $$8x\left(x+3\right)\left(x-5\right)$$  

• $$\left(4x-3\right)\left(2x-5\right)$$  

• $$2\left(2x-3\right)\left(2x+5\right)$$  

• $$4\left(x-3\right)\left(2x+5\right)$$  

Multiple Choice

Factor completely: x²-6x+8

• (x-2)(x-4)
• (x-1)(x-8)
• (x+2)(x+4)
• (x+1)(x+8)

Multiple Choice

Factor completely:
 3x² + 5x - 12

• (3x + 4)(x-3)
• (3x - 4)(x + 3)
• (3x + 3)(x -4)
• (3x - 3)(x + 4)

Multiple Choice

• (x + 9)(x - 3)

• (x + 3)(x - 9)

• (x - 3)(x - 9)

• (x + 3)(x + 9)

Multiple Choice

Which is one of the Factors of the Trinomail.

• (x - 2)

• (x + 1)

• (x + 3)

• (x - 3)

Multiple Choice

Factor the polynomial:
5x² - 13x + 6

• (x + 3)(5x - 2)

• (x - 2)(5x - 3)

• (x + 2)(5x + 3)

• (x - 3)(5x + 2)

Multiple Choice

Factor:
 2m² + 3m - 9

• 2(m + 3)(m - 3)

• (2m - 3)²

• (m + 3)(2m - 3)

• (2m + 3)(m - 3)

Multiple Choice

Factor 9x² + 12x + 4

• (3x+4)(3x+1)

• (9x+1)(x+4)

• (3x+2)²

• (6x+3)(x+1)

Multiple Choice

In order to factor the trinomial ,  $$ax^2+bx+c$$  we need to find to integers that....?

• add to c

• add to b

• subtract to b

• subtract to c

Multiple Choice

Factor

a² - a - 12

• (a + 4)(a - 3)

• (a - 4)(a + 3)

• (a + 6)(a - 4)

• (a - 6)(a + 4)

Multiple Choice

Factor

x² + 9x - 36

• (x + 12)(x - 3)

• (x + 9)(x - 4)

• (x - 9)(x - 4)

• (x - 12)(x + 3)

Multiple Choice

Factor

n² + 5n - 6

• (n + 1)(n - 6)

• (n + 2)(n - 3)

• (n - 2)(n - 3)

• (n - 1)(n + 6)

Multiple Choice

Factor:

b² + 8b + 7

• (b + 4)(b + 3)

• (b + 6)(b + 1)

• (b + 7)(b +1)

• (b+9)(b-1)

Multiple Choice

What is the name of a polynomial with only one term?

• monomial
• binomial
• trinomial
• linear

Multiple Choice

What is the name of a polynomial with three terms?

• monomial
• binomial
• trinomial
• cubic

Multiple Choice

What is the name of the degree of a polynomial that has a variable with invisible exponents?
( ex. n  or  n¹ )

• constant
• linear
• quadratic
• cubic

Multiple Choice

What is the name of the degree of a polynomial that has an exponent of 3?
( ex. t cubed or  t ³ )

• constant
• linear
• quadratic
• cubic

Multiple Choice

What is the name of a 5^th degree polynomial ?
( ex. x⁵ or  mn⁴  or  r²s³ )

• constant
• linear
• quadratic
• quintic

Multiple Choice

What are like terms?
Terms that have....

• the same variables
• the same exponents
• the same coefficients
• the same variables and exponents

Multiple Choice

When you combine like terms, what do you do with the exponents?

• Add them
• Multiply them
• Nothing

Multiple Choice

When you multiply polynomials, what do you do with the exponents?

• Add them
• Multiply them
• Nothing

Multiple Choice

Classify by the DEGREE:
4x³ - 5x² + 2x - 1

• 1
• 2
• 3
• 4

Multiple Choice

Which polynomial is written in standard form?

• 8x - 11x²
• 4x³ + 7x - 9
• 12 + 4x
• 13x + 7x² - 9x³ + 12

Multiple Choice

How many terms are in the polynomial x²-2x+5?

• 0
• 1
• 2
• 3

Multiple Choice

Name the polynomial by degree and number of terms.
x²+2x-8

• cubic trinomial
• quadratic binomial
• quadratic trinomial
• cubic binomial

Multiple Choice

Name the polynomial by degree and number of terms.
2x - 3

• linear binomial
• linear monomial
• quadratic binomial
• quadratic monomial

Multiple Choice

4x² - 3x + 5 is classified as a...

• Cubic Monomial
• Cubic Trinomial
• Quadratic Trinomial
• Quadratic Binomial

Multiple Choice

Which pair is an example of like terms?

• 2a and 2b
• x and x²
• 3k and 3k³
• y² and 2y²

Multiple Choice

What are the different parts and/or pieces of a polynomial that are separated by addition or subtraction signs?

• constant

• term

• exponent

• standard form