Factoring Worksheet1 Solution5





In this page factoring worksheet1 solution5 we are going to see solution of some practice questions from factoring worksheet1.

Question 9:

Solve by factoring method 2(x + 1)² – 5 (x + 1) = 12

Solution:

Let y = x + 1

2 y² – 5 y = 12

2 y² – 5 y – 12 = 0

2 y² – 8 y + 3 y – 12 = 0

2 y (y – 4) + 3 (y – 4) = 0

(2 y + 3) (y – 4) = 0

2 y + 3 = 0                          y - 4 = 0

 2 y =- 3                                   y = 4

     y = -3/2

Now we have to apply the values of y in the equation y = x + 1

x + 1 = -3/2                                          x + 1 = 4

 x = (-3/2) – 1                                          x = 4 – 1       

x = (-3-2)/2                                              x = 3

x = -5/2

Verification:

2(x + 1)² – 5 (x + 1) = 12

if x = -5/2

2[(-5/2) + 1]² - 5[(-5/2) + 1] = 12

2 [-3/2]² - 5 [-3/2 ] = 12

(9/2) + (15/2) = 12

  (9 + 15)/2 = 12

   24/2 = 12

     12 = 12

if x = 3

2[3 + 1]² - 5[3 + 1] = 12

2 [4]² - 5 [4 ] = 12

32 - 20 = 12

12 = 12


Question 10:

3 (x – 4)² – 5(x – 4) = 12

Solution:

Let y = x – 4

3 y² – 5 y = 12

3 y² – 5 y – 12 = 0

3 y² – 9 y  +  4 y – 12 = 0

3 y (y – 3) +  4 (y – 3) = 0

(3 y + 4) (y – 3) = 0

3 y + 4 = 0                                y – 3 = 0

  3 y = -4                                      y = 3

    y = -4/3

to find the value of x we have to apply the values of y in the equation x = y + 4

x = (-4/3) + 4                         x = 3 + 4

   = (-4 + 12)/3                       x = 7

   = 8/3

Verification:

3 (x – 4)² – 5(x – 4) = 12

if x = 8/3

3 [(8/3) - 4]² - 5 [(8/3) - 4] = 12

3[(8 - 12)/3]² - 5[(8 - 12)/3] = 12

3 [(-4/3)]² - 5[-4/3] = 12

(16/3) + (20/3) = 12

(16 + 20)/3 = 12

   36/3 = 12

    12 = 12

if x = 7

3 [7 - 4]² - 5 [7 - 4] = 12

3(3)² - 5 (3) = 12

27 - 15 = 12

 12 = 12

factoring worksheet1 solution5 factoring worksheet1 solution5