Factoring Worksheet1 Solution1

In this page factoring worksheet1 solution1 we are going to see solution of some practice questions from factoring worksheet1.

Question 1:

Solve by factoring method (2x + 3)²  - 81 = 0

Solution:

(2x + 3)²  - 81 = 0

Now we are going to compare (2x + 3)² with the algebraic identity (a+b)² = a² + 2 a b + b²

(2x + 3)²  - 81 = 0

(2 x)² + 2 (2 x) (3) + 3² - 81 = 0

4 x² + 12 x + 9 – 81 = 0

4 x² + 12 x – 72 = 0

Now we are going to divide the whole equation by 4

x² + 3 x – 18 = 0

(x + 6) (x – 3) = 0

x + 6 = 0      x – 3 = 0

x = -6             x = 3

Alternate way:

(2x + 3)²  - 81 = 0

(2x + 3)²  = 81

(2 x + 3) = 81

(2 x + 3) = ± 9

2 x + 3 = 9                           2 x + 3 = - 9

2 x = 9 – 3                           2 x = - 9 – 3

2 x = 6                                  2 x = -12

x = 6/2                                   x = -12/2

x = 3                                        x = -6

Verification:

(2x + 3)²  - 81 = 0

if x = 3

(2 (3) + 3)²  - 81 = 0

(6 + 3)²  - 81 = 0

9²  - 81 = 0

81 - 81 = 0

0 = 0

if x = -6

(2 (-6) + 3)²  - 81 = 0

(-12 + 3)²  - 81 = 0

(-9)²  - 81 = 0

81 - 81 = 0

0 = 0

Question 2:

Solve by factoring method 3 x² – 5 x – 12 = 0

Solution:

3 x² – 5 x – 12 = 0

3 x² – 9 x  + 4 x – 12 = 0

3 x (x – 3) + 4 (x – 3) = 0

(3 x +  4) (x - 3) = 0

3 x + 4 = 0                 x – 3 = 0

3 x = -4                          x = 3

x = -4/3

Verification:

3 x² – 5 x – 12 = 0

if x = 3

3 (3)² – 5 (3) – 12 = 0

3(9) - 15 - 12 = 0

27 - 27 = 0

0 = 0

if x = -4/3

3 (-4/3)² – 5 (-4/3) – 12 = 0

(16/3) + (20/3) - (36/3) = 0

(16 + 20 - 36)/3 = 0

(36 - 36)//3 = 0

0/3 = 0

0 = 0

factoring worksheet1 solution1 factoring worksheet1 solution1