Review on Factoring Polynomials and RAE

Review on Factoring Polynomials and Operations on RAE

Recall! Factoring by GCF

Multiple Choice

What is the GCF of the trinomial?
3x² - 9x -120

• 3

• 2

• 6

• 9

Multiple Choice

What is ALWAYS the first step when factoring?

• Look for the GCF

• Write a, b, and c

• Difference of squares

• Group

Multiple Choice

8r³ - 16r²

• 4r²(2r - 4)

• 8r²(r - 2)

• 8(r³ - r²)

• 4(r³ - 2r²)

Multiple Choice

Factor by using GCF:

8n³ + 2n²

• 2n²(4n-1)

• 2n²(4n + 1)

• n²(8n+2)

• 3n(4n+1)

Multiple Choice

Factor 7x + 21 using the GCF.

• 7(x+3)

• 7x + 3

• 3(x + 7)

• x(7 + 3)

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Recall! Factoring by Grouping

Multiple Choice

Factor by grouping:
x³+7x²-2x-14

• (x²-2)(x-7)

• (x²+2)(x-7)

• (x²+2)(x+7)

• (x²-2)(x+7)

Multiple Choice

Factor by grouping:

4p³ + 8p² + 3p + 6

• (2p²+3)(p+2)

• (2p²+6)(p+4)

• (4p²+3)(p+2)

• (4p²+8p)(3p+6)

Multiple Choice

Factor 28x² + 63x + 12x + 27 by grouping. Remember to look for common factors first.

• (4x + 3)(7x + 9)

• (7x + 3)(4x + 9)

• (3x + 7)(4x + 9)

• (9x + 4)(3x + 7)

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Recall! Factoring DOTS

Multiple Choice

Factor:

$$x^2-49$$  

• $$\left(x+7\right)\left(x-7\right)$$  

• $$7\left(x-7\right)$$  

• $$\left(x-7\right)\left(x-7\right)$$  

• $$x\left(x-7\right)$$  

Multiple Choice

Factor: x² - 400

• (x - 200) (x + 200) 

• (x + 20) (x + 20) 

• (x + 40) (x - 10)

• (x - 20) (x + 20) 

Multiple Choice

Which of the following is NOT a perfect square?

• 1

• 4

• 100

• 8

Multiple Select

Which is an example of difference of two squares?

• ( x³ - 4)

• ( x² - 3)

• ( x² + 4)

• ( x² - 4)

Multiple Choice

Factor 4x²-9

• (4x-9)(4x+9)

• (2x-3)(2x+3)

• 2x-3

• (2x-4.5)(2x+4.5)

Multiple Select

If the area of your garden is ( d^{2 _} 16 ) and the length is

( d + 4) , what is the width?

• ( d+ 2)

• ( d - 2)

• ( d + 4)

• (d - 4)

Multiple Choice

We can't factor using difference of two square this

49x² + 4y². Why?

• Because 4 is not a perfect cubed number.

• Because 4 is not a perfect squared number.

• Because 49 is not a perfect squared number.

• Because we can't factor using difference of two squares if it is addition sign.

Multiple Choice

Factor $$m^2\ -\ 36$$

• $$(m+18)(m-18)$$  

• $$(m+6)^2$$  

• $$\left(m\ -\ 6\right)^2$$  

• $$(m\ +\ 6)\left(m\ -\ 6\right)$$  

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Recall! Factoring DOTC/SOTC

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Recall! Factoring DOTC/SOTC

Multiple Choice

Identify what kind of expression is shown.

• Square of a Binomial

• Difference of Two Squares

• Product of Sum and Difference of Two Cubes

• Sum or Difference of Two Cubes

Multiple Choice

Factor:  27x³ + 8

• (3x + 2)(9x² - 6x + 4)

• (9x + 2)(3x² + 18x + 4)

• (3x²+4)(9x + 2)

• (27x + 8)(x² - 216x + 64)

Multiple Choice

Fully Factor the Following
8x³-27

• (2x+3)(4x²-6x+9)

• (2x-3)(4x²+6x+9)

• (2x-3)(4x²+6x-9)

• (2x-3)(2x²+6x+9)

Multiple Choice

Factor this difference of cubes:
x³ - 343

• (x + 7) (x² - 7x + 49)

• (x² + 1) (x - 343)

• (x - 7) (x² + 7x + 49)

• (x² - 343) (x + 1)

Multiple Choice

Which number is both a perfect square and a perfect cube?

• 64

• 27

• 81

• 16

Multiple Choice

x³ - 1000

• (x + 10)(x² - 10x + 100)

• (x - 10)(x² + 10x + 100)

• (x - 1)(x² + 1x + 1)

• (x - 5)(x² + 5x + 25)

Multiple Choice

Factoring the sum or difference of two cubes can be used ONLY if the two terms of the binomials have perfect square roots.

• TRUE

• FALSE

Multiple Choice

Complete the formula
a³-b³=

• (a-b)(a²+ab+b²)

• (a+b)(a²-ab+b²)

• (a-b)(a²-ab+b²)

• (a+b)(a²+ab+b²)

Multiple Choice

Complete the formula

a³+b³=

• (a-b)(a²+ab+b²)

• (a+b)(a²-ab+b²)

• (a-b)(a²-ab+b²)

• (a+b)(a²+ab+b²)

Multiple Choice

Factor: 8x³ - 1

• (2x - 1)(4x² + 2x + 1)

• (2x + 1)(4x² - 2x + 1)

• (2x - 1)(4x² - 2x - 1)

• (2x + 1)(4x² +2x + 1)

Multiple Choice

Factor:   x³ + 1

• (x + 1)³

• (x+1)(x² - x + 1)

• (x - 1) (x² + x - 1)

• (x + 1)(x² - 2x + 1)

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Recall! Factoring Quadratic Trinomials

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Recall! Factoring Quadratic Trinomials

Multiple Choice

Factor 

$$k^2+7k+10$$  .

• $$(k+2)(k-5)$$  

• $$(k+2)(k+5)$$  

• $$(k+10)(k+4)$$  

• $$(k-2)(k-5)$$  

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
3v² - 4v - 7

• (3v-7)(v+1)
• 3(v-7)(v-1)
• (3v+1)(v-9)
• (3v+1)(v-10)

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:
 4h² - 17h + 4

• (2h - 2)²

• 4(h + 4)(h + 1)

• (2h - 2)(2h + 2)

• (h - 4)(4h - 1)

Multiple Choice

Factor $$k^2-2k-24$$  

• $$(k-4)(k+6)$$  

• $$(k+4)(k+6)$$  

• $$(k+6)(k-1)$$  

• $$(k+4)(k-6)$$  

Multiple Choice

Factor:

$$x^2+6x+8$$  

• $$(x+4)(x+3)$$  
  

• $$(x+2)(x+3)$$  
  

• $$(x+4)(x+2)$$  
  

• $$(x+5)(x+1)$$  
  

Multiple Choice

Factor

$$x^2-10x+16$$  

• $$(x+12)(x-2)$$  
  

• $$(x-4)(x-6)$$  
  

• $$(x+10)(x-2)$$  
  

• $$(x-2)(x-8)$$  
  

Multiple Choice

Factor Completely
$$n^2-12n+35$$  

• $$4\left(n+9\right)\left(n+10\right)$$  

• $$\left(n-7\right)\left(n-5\right)$$  

• $$\left(n-7\right)\left(n+5\right)$$  

• Not Factorable

Multiple Choice

Factor Completely
$$m^2-6m-27$$  

• $$\left(m+7\right)\left(m-2\right)$$  

• $$\left(m+3\right)\left(m-9\right)$$  

• $$6m\left(m+8\right)$$  

• $$\left(m+3\right)\left(m+9\right)$$  

Multiple Choice

Factor
x² - 5x - 36

• (x - 4)(x + 9)
• (x - 6)(x + 6)
• (x + 4)(x - 9)
• (x -12)(x + 3)

Multiple Choice

Factor: x² + 2x – 3

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

Multiple Choice

Factor
a² - a - 12

• (a - 4)(a + 3)
• (a + 6)(a - 4)
• (a - 6)(a + 4)
• (a + 4)(a - 3)

Multiple Choice

2) Factor: m² + 8m + 15

• (m + 2)(m +6)

• (m + 1)(m + 7)

• (m + 4)(m + 4)

• (m + 3)(m + 5)