factorise 2x⁴ - 162 (step by step)
Answers
2x4 - 162 = 0
2x4 - 162 = 2 • (x4 - 81)
- Factoring: x4 - 81
- check : 81 is the square of 9
- 81 is the square of 9Check : x4 is the square of x2
81 is the square of 9Check : x4 is the square of x2 Factorization is : (x2 + 9) • (x2 - 9)
Factoring: x2 - 9
Factoring: x2 - 9 Check : 9 is the square of 3
Factoring: x2 - 9 Check : 9 is the square of 3Check : x2 is the square of x1
Factoring: x2 - 9 Check : 9 is the square of 3Check : x2 is the square of x1 Factorization is : (x + 3) • (x - 3)
2 • (x2 + 9) • (x + 3) • (x - 3) = 0
☞Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
☞Solve : x2+9 = 0
Subtract 9 from both sides of the equation :
x2 = -9
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ -9
The prime factorization of 9 is 3•3
√ 9 = √ 3•3
= ± 3 • √ 1
= ± 3
☞Solve : x+3 = 0
Subtract 3 from both sides of the equation :
x = -3
☞Solve : x-3 = 0
Add 3 to both sides of the equation :
x = 3