M8: Using Factors to Solve Quadratic Equations

Question 1

What solving method would you use to solve this equation?

4x^2 + 4x + 1

Answer 1

To solve easily, use the box method.

Question 2

(x+6) (x-4)

Answer 2

x^2+2x-24

Question 3

(2x+5) (x-3)

Answer 3

2x^2-x-15

Question 4

(x-6) (x+1)

Answer 4

x^2-5x-6

Question 5

(x^2+3) (x-4)

Answer 5

x^3-4x^2+3x-12

Question 6

(x^2+11) (x+6)

Answer 6

x^3+6x^2+11x+66

Question 7

(x^2+8) (x-5)

Answer 7

x^3-5x^2+8x-40

Question 8

(x+3) (x+7)

Answer 8

x^2+10x+21

Question 9

(4x+2) (x-2)

Answer 9

4x^2-6x-4

Question 10

(3x+2) (2x+5)

Answer 10

6x^2+19x+10

Question 11

(x^2-6) (x-4)

Answer 11

x^3-4x^2-6x+24

Question 12

(x^2+9) (x-3)

Answer 12

x^3-3x^2+9x-27

Question 13

(4x^2-4) (2x+1)

Answer 13

8x^3+4x^2-8x-4

Question 14

(x-3) (x^2+2x+1)

Answer 14

x^3+x^2-5x-3

Question 15

(x+5) (x^3+6x^2+18x)

Answer 15

x^4+11x^3+48x^2+90x

Question 16

(x+4) (x^4+x^2+1)

Answer 16

x^2+x^3+x

Question 17

Zero Product Property

Answer 17

set equation = to 0

Question 18

Diamond Method

Answer 18

Diamond shape where you multiply a and c together and put them at the top point of the diamond then b at the bottom. To find the numbers on the side you must find 2 numbers that multiply to ac and also add to b.

Question 19

What method should you use for the following equation : ax^2+bx+c

Answer 19

Diamond Method

Question 20

x^2 + x - 6 = 6

Answer 20

Answer is x= -4 x= 3
Steps:
x^2 + x - 12 = 0
(x + 4)(x - 3) = 0
x + 4 = 0  x-3 = 0
x = -4       x = 3

Question 21

x^2 - 3x - 5 = 5

Answer 21

Answer is x = -2   x = 5
Steps:
x^2 - 3x - 10 = 0
(x+2)(x-5)=0
x+2 = 0   x - 5 = 0
x= -2         x = 5

Question 22

36x^2 + 84x + 40 = -9

Answer 22

Answer is x = -7/6
Steps: 
(Squiggle Line Method)
36x^2 + 84x + 49 = 0 
~~~~                ~~~~
6x                      7
               42x
(6x+7)^2 = 0
6x + 7 = 0
6x = -7
x = -7/6

Question 23

4x^2 + 12x = -8

Answer 23

Answer is x = -1 ,  x = -2
Steps:
4x^2 + 12x + 8 = 0
4(x^2 + 3x + 2) = 0
4(x + 1) (x + 2) = 0
x + 1 = 0       x + 2 = 0
x = -1            x = -2
x = -1   ,  x = -2

Question 24

x^2 + 8x + 16 = 33

Answer 24

Answer is x = -23  x = -9
Steps:
8/2  = 4^2 = 16
x^2 + 8x + 16 = 49
(x + 4)^2  = 49
x+16 = +/- √49
x+ 16 = +/- 7
-16=        -16
x = -16 +/-7
x=-16-7         x=-16+7
x=-23             x=-9

Question 25

Steps to finding what equation to use

Answer 25

1. Get Equation to 0
2. Identify A,B,C
3. Check if A and C are perfect squares
   ( If so we can apply our shortcuts)
4. If A = 1 check if the reverse box method is possible
5. If A is other than 1 try the diamond method
6. Use completing the Square if there are negative numbers.
7. Use the Quadratic formula when there are more fractions or positive numbers