factorize : 36x^3-x
Answers
Answer:
= x (36x² -1)
Step-by-step explanation:
= 36x³ - x
= x (36x² -1)
Answer:
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(22•32x3) - x = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
36x3 - x = x • (36x2 - 1)
Trying to factor as a Difference of Squares:
3.2 Factoring: 36x2 - 1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 36 is the square of 6
Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (6x + 1) • (6x - 1)
Equation at the end of step
3
:
x • (6x + 1) • (6x - 1) = 0
STEP
4
:
Theory - Roots of a product
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
4.2 Solve : x = 0
Solution is x = 0
Solving a Single Variable Equation:
4.3 Solve : 6x+1 = 0
Subtract 1 from both sides of the equation :
6x = -1
Divide both sides of the equation by 6:
x = -1/6 = -0.167
Solving a Single Variable Equation:
4.4 Solve : 6x-1 = 0
Add 1 to both sides of the equation :
6x = 1
Divide both sides of the equation by 6:
x = 1/6 = 0.167