Factors & Quadratic Equations

Factoring & Solving
Quadratic Equations

Dr. Tom Giles

Factoring

Factoring using a GCF

(Greatest Common Factor)

Multiple Choice

Factor by using GCF:
8n³ + 2n²

• 2n²(4n-1)
• 2n²(4n + 1)
• n²(8n+2)
• 3n(4n+1)

Multiple Choice

Factor by using GCF:
$$4x^3+16$$

• 2x²(4x-1)

• 4x(x + 4)

• x²(8x+2)

• 3x(4x+1)

Be sure to Check all choices.

When there appear to be 2 correct choices - pick the choice that is the larger factor (biggest number on the outside of parenthesis).

Trinomial Factoring

Trinomial Factoring

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
n² + 5n - 6

• (n - 2)(n - 3)
• (n - 1)(n + 6)
• (n + 1)(n - 6)
• (n + 2)(n - 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
a² - a - 12

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

Multiple Choice

Factor
3v² - 4v - 7

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

Finding One of the Factors

• Sometimes you may be asked to find "One" of the factors.

Multiple Choice

Factor:

x² + 9x - 36

• (x + 12)(x-3)

• (x + 9)(x-4)

• (x - 12)(x+3)

• (x - 9)(x+4)

Multiple Choice

What are the solutions for:

a² - a - 12

• a= - 2

  a= -6

• a= - 4

  a= +3

• a= + 4

  a= -3

• a= +6

  a= -6

Multiple Choice

What are the solutions for:

2n² + 14n - 16

• n= - 8

  n= +1

• n= +8

  n= -1

• n= +4

• None of these

Multiple Choice

What are the solutions for:

3a² + 4a + 1

• a= 3

  a= 1

• a= 4

  a= 1

• a= -1

  a= -1/3

• a= 1

  a= 1/3

Factoring Completely

Sometimes you have to find a GCF first, then factor again.

Multiple Choice

50m³ - 2m 

• 2m(25m²-1)
• 2m(5m-1) (5m-1)
• 2m(5m-1) (5m+1)
• PRIME

Multiple Choice

3x³ + 15x² + 18x

• 3x(3x + 9)(x - 15)

• 3x(x+3)(x+2)

• x(x - 5)(x + 5)

• 3x(x-3)(x - 3)

Multiple Choice

5m² -20m - 25

• 5(m+1) (m-5)

• (3m-5) (5m+5)
• 5(3m²-2m-5)
• PRIME

Multiple Choice

8x³ - 18x

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

• (4x²+3) (2x-3)
• 2x(2x+3) (2x-3)
• PRIME