Unit 6.1 Review (Day 1)

Today you will be working through practice questions. Some of the questions require you to work on a whiteboard, some questions you can complete in your head. Once you have completed the assignment, make sure all other work from Unit 5.1 has been completed.

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Unit 5.1 Review

(Day 1)

Part 1: Standard Form of a Polynomial

Multiple Choice

$$13x^2\ -\ 5\ +\ 6x^{3\ }-\ x$$  

Which answer represents the polynomial in standard form?

• $$-5\ -\ x\ +\ 13x^2\ +\ 6x^3$$  

• $$6x^{3\ }+\ 13x^2\ -\ 5\ -\ x$$  

• $$13x^2\ -\ 5\ +\ 6x^{3\ }-x$$  

• $$6x^{3\ }+\ 13x^2\ -x\ -\ 5$$  

Multiple Choice

What is the leading coefficient? 

(*Hint: Remember to write the polynomial in standard form first)

5x²+3x³-2x+1

• 5

• 3

• -2

• 1

Multiple Choice

Which polynomial is written in standard form?

• -3x + 8x² + 9x³ - 11

• 9x³ + 8x² - 3x - 11

• 8x² + 9x³ -11 - 3x

• -11 - 3x + 8x² + 9x³

Part 2: Greatest Common Factors

Multiple Choice

What is the greatest common factor of 10 and 25?

• 5

• 1

• 10

• _¹

Multiple Choice

What is the greatest common factor of 18k and 15k³

• 3k²

• 3k³

• 3k

• 5k

Multiple Choice

What is the greatest common factor of

3x(x + 2) - 7(x + 2)

• (x + 2)

• (3x - 7)

• x

• 3x² - x -14

Part 3: Addition, Subtraction and Multiplication

Multiple Choice

Find the difference. 
(3- 2x + 2x²) - (4x -5 +3x²)

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Multiple Choice

(4x + 7)(3x + 5)

• 12x + 41 + 35

• 12x² + 20x + 35

• 12x² + 41x + 35

• 12x + 20 + 35

Multiple Choice

(x+4)²

• x²+16

• x²-16

• x²+8x+16

• x²+8x-16

Multiple Choice

(x-3)(x²+2x+7)

• x³-x²+x-21

• x³+5x+13x-21

• x³-3x²+7x-21

• x²+2x-3

Multiple Choice

Add: (3x² + 2x + 1) + (2x² - 4x - 5) + (3x - 1)

• 5x² + 6x - 7

• 8x² - 3x - 5

• 5x² + x - 5

• 6x² + 8x + 5

Multiple Choice

Find the sum.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

• 4x³ + 1x² – 3x + 1

• 2x³ + 1x² - 5x + 9

• 6x³ + 1x - 1x² - 3

• 3x⁵ +1x - 1x⁵ - 3x

Multiple Choice

Simplify the expression.
2x(-2x - 3)

• -4x - 3

• x² - 3

• -4x² - 6x

• -4x - 6

Multiple Choice

(2x-9)(2x+4)

• $$4x^2+4x+4$$  

• $$2x^2-9x+4$$  

• $$4x^2-10x-36$$  

• $$4x^2-26x-36$$  

Multiple Choice

$$\left(m+5\right)\left(m^2+4m-8\right)$$  

• $$m^3+4m^2-8m+5m^2+20m-40$$  

• $$m^2+40m+m^3$$  

• $$m^3+9m^2+12m-40$$  

Multiple Choice

4a(5a² - a + 4)

• 20a³ - 4a² + 16a

• 20a² - 5a + 8a

• 20a² + 4a² + 16a

• 20a³ +3a² + 16a

Multiple Choice

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

• 3y³ + 7y² - 4y + 3

• 4y² + 3y³ - y + 3

• -y⁴ + 2y³ -y - 4

• 4y³ + 3y² -3y + 1

Multiple Choice

A rectangle has width (2x + 3) and length (2x - 4).  What is the perimeter of the rectangle?

• 4x - 12

• 4x - 1

• 8x - 2

• 4x² - 2x - 12

Multiple Choice

Find the area of the rectangle.

• 8x² + 14x + 6

• 12x + 10

• 8x² + 6

• 6x² + 14x + 6

Part 4: Factor each polynomial completely

Multiple Choice

Factor out the GCF:
12x + 6

• 6(2x + 1)

• 3(4x + 2)

• 6x(2x + 1)

• 2(6x + 3)

Multiple Choice

Factor out the GCF:
10x³ - 15x

• x(10x² - 15)

• 5x(2x² - 3)

• 5(2x³ - 3x)

• 5x²(10x - 3)

Multiple Choice

Factor
k²+7k+10

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)

Multiple Choice

factor:x² - 25

• ( x + 5 ) ( x - 5 ) 

• ( x - 5 ) ( x - 5 ) 

• ( x + 5 ) ( x + 5 ) 

• Prime

Multiple Choice

Factor Completely: 
3x² + 18x +15

• 3(x² + 6x + 5)

• (x + 5)(x + 1)

• 3(x + 5)(x + 1)

• Prime

Multiple Choice

Factor:
x² + 7x - 30

• (x + 10)(x - 7)

• (x - 10)(x + 3)

• (x + 10)(x + 3)

• (x + 10)(x - 3)

Multiple Choice

Factor x²-2x-15

• (x+5)(x-3)

• (x-5)(x-3)

• (x-5)(x+3)

• (x+5)(x+3)

Multiple Choice

What are the factors of
25x² - 81?

• (5x - 9)(5x + 9)

• (5x - 9)(5x - 9)

• (5x + 9)(5x + 9)

• Cannot be factored

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

Factor by grouping:
3x³-x²+6x-2

• (x²+2)(3x+1)

•  (x²+2)(3x-1)

• (3x³+6x)(x²-2)

• none of the aboe

Multiple Choice

Factor completely: 2x²+22x+60

• (2x+10)(x+6)

• (x+5)(x+6)

• 2(x+1)(x+30)

• 2(x+5)(x+6)

Multiple Choice

Factor:
x² - 9

• (x + 3)(x - 3)

• (x + 3)²

• (x - 3)²

• (x+3)(x+3)

Multiple Choice

20x³-25x²+4x-5

• (5x²-5)(4x+1)

• 5(x²-1)(4x+5)

• (5x²+1)(4x-5)

• (5x²+1)(4x-1)

Multiple Choice

30x³+15x²-18x-9

• (5x²-3)(6x+1)

• (5x²-3)(6x+3)

• 3(5x²+3)(2x-1)

• 3(5x²-3)(2x+1)

Multiple Choice

Factor by grouping
x³ - 4x² -4x + 16

• (x+4)(x+2)

• (x-4)(x² -4) 

• (x+4)(x² -4)

• (x-4)(x-2)

Multiple Choice

Factor:

6x² + 2x – 21x – 7

• (2x +7)(3x – 1)

• (1x – 1)(6x+7)

• (2x – 7)(3x+1)

• (6x – 7)(1x+1)

Multiple Choice

Factor

3a² + a + 3a + 1

• (7a-10)(a-8)

• Not factorable

• (3a+1)(a+1)

• (3a-1)(a-1)

Multiple Choice

Factor: 6x² + 21x + 4x + 14

• (3x - 2)(2x - 7)

• 4(2x + 5)(3x - 4)

• (3x + 2)(2x + 7)

• 6(x + 2)(x - 7)

Multiple Choice

Factor by grouping
x³ - 4x² -4x + 16

• (x+4)(x+2)

• (x-4)(x² -4) 

• (x+4)(x² -4)

• (x-4)(x-2)

Multiple Choice

Factor x² + 7x + 12

• (x + 2)(x + 10)
• (x + 3)(x + 4)
• (x + 4)(x + 5)
• (x + 4)(x + 6)

Multiple Choice

Factor:
x² + 7x - 30

• (x + 10)(x - 7)
• (x - 10)(x + 3)
• (x + 10)(x + 3)
• (x + 10)(x - 3)

Multiple Choice

Factor
x² + 9x - 36

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

Multiple Choice

Factor
n² + 5n - 6

• (n - 2)(n - 3)
• (n - 1)(n + 6)
• (n + 1)(n - 6)
• (n + 2)(n - 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

Factor
r² -16r + 60

• (r - 15)(r + 4)
• (r - 6)(r + 10)
• (r - 6)(r - 10)
• (r +30)(r - 2)

Multiple Choice

Factor
x² -16x + 48

• (x - 12)(x - 4)
• (x + 6)(x - 8)
• (x + 12)(x - 4)
• (x -16)(x - 3)

Multiple Choice

Factor:
p² - 14p

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

Multiple Choice

Factor:
x² -15x + 36

• (x - 18)(x + 2)
• (x - 12)(x - 3)
• (x - 12)(x + 3)
• (x + 18)(x - 2)

Multiple Choice

Which is another way of correctly expressing
 (x  - 3)(x - 3)?

• (x² - 3²)
• (x² - 3)
• (x + 3)(x - 3)
• (x - 3)²

Multiple Choice

Factor:
x² - 8x - 128

• (x - 16)²
• (x - 16)(x + 8)
• (x + 16)(x - 8)
• (x - 16)(x - 8)

Multiple Choice

x² + 5x + 6

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

Multiple Choice

Factor
n² + 16n + 63

• (n-7)(n+4)
• (n+7)(n-9)
• (n-3)(n-10)
• (n+7)(n+9)

Multiple Choice

Factor: x² – 5x – 24

• (x - 5)(x + 19)
• (x - 8)(x + 3)
• (x - 3)(x + 8)
• (x - 19)(x + 5)

Multiple Choice

Factor the Trinomial:
x² - 8x + 15

• (x + 5) ( x + 3)
• (x - 5) (x - 3)
• (x + 15) (x - 1)
• (x - 7) (x - 8)

Multiple Choice

x² - 16

• Prime

• ( x - 4) ( x + 4) 

• ( x - 8) ( x + 8) 

• ( x - 4) ( x - 4) 

Multiple Choice

Factor:
x² - 5x

• 1(x - 5)

• x(x - 5x)

• x(x - 5)

• x²(1 - 5)

Multiple Choice

Factor
n²-13n+40

• (n-5)(n-8)

• (n+5)(n-8)

• (n-5)(n+8)

• (n+6)(n+1)

Multiple Choice

Factor: x² + 2x – 3

• (x - 2)(x + 1)

• (x + 1)(x - 3)

• (x + 2)(x - 1)

• (x - 1)(x + 3)