Factoring: Expressions with 4 terms

Factoring: Expressions with 4 Terms Lesson

By Grouping and Box Method

Some foundational information

Vocabulary

Binomial Factor

Binomial factors are polynomial factors that have exactly two terms. (x-r) represents a binomial factor.

Factored Form

Factored form, the product of a constant and two linear terms:...a is the constant... (x-r) is a binomial factor...r is the root/x-intercept. Converting a quadratic function to factored form is called factoring.

Factor By Grouping Video Link

https://www.youtube.com/watch?v=NYMpf4fdnbY

Factor by Grouping Example

• Divide the expression into two groups inside ( ).

• Each part should have a common binomial factor...same two terms inside ()

• Factor out the Common Binomials

• You should have the factored form of the expression...two binomial factors

Multiple Choice

Factor by grouping

x³ - 4x² - 4x + 16

Hint: the answer is not completely factored

• (x + 4)(x² - 4)

• (x + 4)(x + 2)

• (x - 4)(x - 2)

• (x - 4)(x² - 4)

Multiple Choice

Factor by grouping:

4p³ + 8p² + 3p + 6

• (2p² + 6)(p + 4)

• (2p² + 3)(p + 2)

• (4p² + 8p)(3p + 6)

• (4p² + 3)(p + 2)

Multiple Choice

Factor

 $16mn-4m^2+28n-7m$  by grouping

• (4m+7)(4n-m)

• (4m-7)(4n-m)
  
  

• (4m-7)(4n+m)

The Box Method

When given a Quadratic Trinomial

Box Method Vedeo Link

https://www.youtube.com/watch?v=OKkg2kUsDq4&t=44s

Box Method

• Factor the GCF from each row and column

• The column and row of factors will be the binomial factors of the trinomial.

• (x+2)(2x+5) is the factored form of the original expression

Multiple Choice

What expressions should replace A and B?

• A = 2 and B = -1

• A = 2x and B = -1

• A = 2x² and B= -5

• A = 2x and B = -5

Multiple Choice

Factor using box method

x³ - 4x² - 4x + 16

Hint: the answer is not completely factored

• (x + 4)(x² - 4)

• (x + 4)(x + 2)

• (x - 4)(x - 2)

• (x - 4)(x² - 4)

Multiple Choice

Factor by box method:

4p³ + 8p² + 3p + 6

• (2p² + 6)(p + 4)

• (2p² + 3)(p + 2)

• (4p² + 8p)(3p + 6)

• (4p² + 3)(p + 2)

Multiple Choice

Factor

 $16mn-4m^2+28n-7m$  by grouping

• (4m+7)(4n-m)

• (4m-7)(4n-m)
  
  

• (4m-7)(4n+m)

Multiple Choice

Given the expression

 $3x^2+13x+12$ . Determine the values that would fill in boxes B and C.

• 8 and 5

• 9 and 4
  
  

• 15 and -2

• 3 and 12

Multiple Choice

3x² + 8x + 5

• (x - 1) (3x - 5)

• (3x - 1) (x - 5)

• (x + 1) (3x + 5)

• (3x + 1) (x + 5)

Multiple Choice

Factor: 2x² - 5x + 2

• (2x + 1)(x - 2)

• (2x - 2)(x - 1)

• (2x - 1)(x - 2)

• (2x + 2)(x - 1)

Multiple Choice

Factor 12xy − 28x − 15y + 35

• (4x-5)(3y+7)

• (4x+5)(3y-7)

• (4x-5)(3y-7)