Unit 9 Content Recovery

Unit 9: Factoring Polynomial expressions

Content Recovery

By Hannah Wiley

Multiple Choice

Factor
10x² + 15x-5

• 25(10x³+45x-15)
• 5(2x³ + 3x²-x)
• x(10x³+15x-5)
• 5(2x²+3x-1)

Multiple Choice

Factor:
 2n²-8n³

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

Multiple Choice

Factor
4b⁵+4b³+16b²

• 4b³(b⁴+b²+4b)
• 4b³(b⁴+4b+5)
• 4(b⁵+b³+4b²)
• 4b²(b³+b+4)

Multiple Choice

Factor by GCF:

6m² + 16m

• 2(3m² + 8m)

• 2m(3m + 8)

• 2m(3m - 8m)

• Prime

Multiple Choice

Factor by GCF:

17xy - x

• 17(xy - x)

• y(17x - x)

• x(17y - 1)

• Prime

Multiple Choice

What is the GCF of 18k and 15k³

• 5k³

• 3k³

• 3k

• 5k

Multiple Choice

What is the greatest common factor of the three terms in the expression?
24m³n⁵p + 6mn⁴p² + 4mn⁵

• 2mn
• 24mn⁴
• 2mn⁴
• 2mn⁴p

Multiple Choice

What is the GCF?
15x + 27

• 3
• 5
• 9
• 2

Multiple Choice

Factor the polynomial
12x - 9 

• 3x(4x - 3)
• 6(2x - 1)
• 3(4x - 3)
• 3(x - 3)

Multiple Choice

Which of these can factor using difference of two squares?

• 144x² - 49y²

• x² + 4x - 12

• 100x² + 20x + 1

• 14x - 16

Multiple Choice

Which one is false about the difference of two squares?

• We can factor because there is addition sign.

• We can factor because there is a perfect squared number (Example: x², 25, 49)

• Formula: a² - b² = (a + b) (a - b)

• We can factor because there is minus sign.

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 completely.

49x² + 16

• ( 7x + 4 ) ( 7x - 4 )

• ( 7x + 4 ) ( 7x + 4 )

• ( 7x - 4 ) ²

• does not factor (SUM of squares)

Multiple Choice

Factor 4x²-9

• (4x-9)(4x+9)

• (2x-3)(2x+3)

• 2x-3

• (2x-4.5)(2x+4.5)

Multiple Choice

Fully Factor the Following
25x²-81

• (5x-9)²
• (5x+9)(5x-9)
• 25(x-9)²
• (9x+5)(9x-5)

Multiple Choice

9x² - 49y⁶

• ( 3x + 7y³) (3x + 7y³) 
• ( 3x - 7y³) (3x + 7y³) 
• ( 3x - 7y³) (3x - 7y³) 
• Prime

Multiple Choice

16p³ - 81q⁶

• (4p + 9q) (4p - 9q)
• (4p² + 9q³) (4p - 9q³)
• (4p² + 9q) (4p - 9q)
• Can't factor using Diff. of Squares

Multiple Choice

r⁴ - q⁴

• (r² + q²) (r² - q²)
• (r² - q²) (r² - q²)
• (r + q) (r - q)
• Can't factor using Diff. of Squares

Multiple Choice

9n² + 1

• (3n + 1) (3n - 1)
• (3n - 1) (3n - 1)
• (n + 3) (n - 3)
• Can't factor using Diff. of Squares

Multiple Choice

3x² - 75

• 3( x + 5 ) ( x - 5 ) 
• Prime
• ( x + 5 ) ( x - 5 ) 
• 3( x - 5 ) ( x - 5 ) 

Multiple Choice

32n² - 50
(Check for a GCF)

• (16n - 25)(16n + 25)
• 2(8n - 25)(8n + 25)
• 2(4n + 5)(4n - 5)
• Not Factorable

Multiple Choice

The following are examples of quadratic trinomials EXCEPT:

• $$x^2+2y+1$$

• $$3a-2a+4$$

• $$2y^2+x-4$$

• $$z^2-5z+6$$

Multiple Choice

To factor

$$x^2+8x+15$$  , find two factors of 15 whose sum is _____.

• 1

• 2

• 8

• 15

Multiple Choice

To factor

$$x^2-10x-24$$ , which of the following factors of $$-24$$  must be chosen in the process?

• $$-2,\ 12$$  

• $$-6,\ -4$$  

• $$2,\ -12$$  

• $$-6,\ 4$$  

Multiple Choice

What do you call a polynomial that cannot be factored?

• FOIL
• Simplified
• Prime
• Proper

Multiple Choice

What has a product of 6 and has a sum of 5

• 2 and 3

• 6 and 1

• 5 and 1

• 4 and 2

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
k² - 2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)

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 + 16n + 63

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

Multiple Choice

Factor
x² - 5x - 36

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