Factoring Polynomials

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

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

• 64

• 27

• 81

• 16

Multiple Choice

Factor x³+8

• (x-2)(x²+2x+4)
• (x+2)(x²-2x+4)
• (x-2)(x²-2x+4)
• (x-2)(x²+2x+2)

Multiple Choice

Factor 8x³+216

• (2x+6)(4x²-12x+36)
• (2x-6)(4x²+12x+36)
• (4x+6)(16x²-24x+36)
• (4x-6)(16x²+24x+36)

Multiple Choice

Factor completely: 4x³ - 20x² - 1x + 5

• (2x - 1)(2x - 1)(x - 5) = 0

• (2x + 1)(2x + 1)(x - 5) = 0

• (2x + 1)(2x - 1)(x + 5) = 0

• (2x + 1)(2x - 1)(x - 5) = 0

Multiple Choice

What is the factored form of 5n³-10n²+3n-6

• (5n²+3)(n-2)
• (5n²-3)(n-2)
• (5n³+3)(n-2)
• 10n(n²-6)

Multiple Choice

Factor
20p²q² - 25pm

• pm(4q - 5m)
• 5(4pq³ - 5m)
• pq(20pq² - 25m)
• 5p(4pq² - 5m)

Multiple Choice

Factor 8x³ + 18x.

• 2x(4x² + 9)
• 8x(x² + 10)
• 2(4x³ + 9x)
• 8(x³ + 10x)

Multiple Choice

Factor 
3x⁴- 12xy

• x(3x³-12y)
• 3x(x³- 4y)

Multiple Choice

Factor 4b⁵ + 4b³ + 16b².

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

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 + 7x + 12 

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

Multiple Choice

Factor
x² - 9x + 18.

• (x - 3)(x - 6)
• (x + 6)(x - 3)
• (x - 9)(x - 2)
• (x - 6)(x + 3)

Multiple Choice

Factor
x² + 4x - 32

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

Multiple Choice

Factor
3x² + 5x - 12.

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

Multiple Choice

Factor
3a² + 4a + 1

• (7a-10)(a-8)
• Not factorable
• (3a+1)(a+1)
• (3a-1)(a-1)

Multiple Choice

Factor: 
3x² + 18x +15
Hint: Factor GCF first.

• 3(x² + 6x + 5)
• (x + 5)(x + 1)
• 3(x + 5)(x + 1)
• Prime

Multiple Choice

Factor Completely:
x² - 36

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

Multiple Choice

Factor 25x² - 81.

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

Multiple Choice

factor completely 
$$81m^4-1$$

• not factorable
• (m-9)(m+9)
• $$\left(9m^2-1\right)\left(9m^2+1\right)$$

• $$\left(3m-1\right)\left(3m+1\right)\left(9m^2+1\right)$$