Factoring and solving quadratics

Factoring and solving quadratics

Factoring

1) Look for a GCF

Multiple Choice

What is the GCF of 18k and 15k³

• 3k²
• 3k³
• 3k
• 5k

Multiple Choice

Factor:

2n²-8n³

• 2n²(n-4n²)

• -2n²(4n²-1)

• 2n³(10-8n²)

• 3n(1-4n)

Multiple Choice

Factor:
10a⁴+16a+10a²

• 2a(5a³⁺8+5a)
• 2a⁴(5a+8a²+5a³)
• 2a⁴(10+16a+40a²)
• 3a³(5+8a+a²)

• If you have 3 terms use the X method

• If there is a number in front of your squared term, slide and divide

Multiple Choice

x² - 9x - 22

• (x + 11) (x - 2)

• (x + 2) (x - 11)

• (x - 11) (x - 2)

• (x + 2) (x + 11)

Multiple Choice

x² - 9x + 18

• (x + 6) (x + 3)

• (x - 6) (x - 3)

• (x - 2) (x - 9)

• (x + 2) (x + 9)

Multiple Choice

x² + 5x + 6

• (x - 3) (x - 2)

• (x + 3) (x - 2)

• (x + 3) (x + 2)

• (x + 2) (x - 3)

Multiple Choice

x² + 8x - 20

• (x + 10) (x - 2)

• (x + 10) (x + 2)

• (x + 5) (x + 4)

• (x + 5) (x - 4)

Multiple Choice

7x² - 16x + 4

• (x + 2) (7x - 2)

• (x + 2) (7x + 2)

• (x - 2) (7x + 2)

• (x - 2) (7x - 2)

Multiple Choice

6x² - x - 1

• (3x - 1) (2x + 1)

• (3x + 1) (2x - 1)

• (6x + 1) (x - 1)

• (6x - 1) (x + 1)

Multiple Choice

3x² + 8x + 5

• (x - 1) (3x - 5)

• (3x - 1) (x - 5)

• (x + 1) (3x + 5)

• (3x + 1) (x + 5)

To solve by factoring

• Use the box method to factor.- make sure everything is on one side and set = 0

• Set each factor = 0 and solve

Multiple Choice

 $n^2-10n+24=0$  

•  $\left\{8,3\right\}$  

•  $\left\{4,6\right\}$  

•  $\left\{-4,-6\right\}$  

•  $\left\{12,2\right\}$  

Multiple Choice

 $b^2+8b-33=0$  

•  $\left\{8,-33\right\}$  

•  $\left\{3,-11\right\}$  

•  $\left\{3,11\right\}$  

•  $\left\{-11,-3\right\}$  

Multiple Choice

 $x^2-24x+114=19$  

•  $\left\{10,14\right\}$  

•  $\left\{-5,-19\right\}$  

•  $\left\{24,\ 19\right\}$  

•  $\left\{5,19\right\}$  

Quadratic Formula

• Make sure your equation is set = 0 and find a, b and c

• Use the formula:

   $x\ =\ \frac{-\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$  

Multiple Choice

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Factor

• Write down: a = 1, b = 6, c = -13

• Subtract 3 from both sides.

• Add 3 to both sides.

Multiple Choice

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Multiple Choice

Solve using the Quadratic Formula:

2x² + x - 4 = 0

• x = -¼ and x = -2

• x = 1.19 and x = -1.69

• x = 8 and x = -4

• x = 1.69 and x = 1.20

Multiple Choice

Solve 2x² + 7x - 15 = 0

• -3/2 or 5

• No Solution

• -5 or 3/2

• 0.7 or 5

Multiple Choice

Use the quadratic formula to solve 2x² + 2x - 12.

• -2, 3

• 2, 3

• 2, -3

• -2, -3