Question

2x-4x/4÷5 solve the following ​

Answer 1

Answer:

2x-4x/4÷5

8x-4x/4÷5

4x/4×1/5

4x/20

Answer 2

Step-by-step explanation:

Step by step solution :

STEP

1

:

Equation at the end of step 1

2x - 22x4 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2x - 4x4 = -2x • (2x3 - 1)

Trying to factor as a Difference of Cubes:

3.2 Factoring: 2x3 - 1

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 2 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(x) = 2x3 - 1

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 2 and the Trailing Constant is -1.

The factor(s) are:

of the Leading Coefficient : 1,2

of the Trailing Constant : 1

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -3.00

-1 2 -0.50 -1.25

1 1 1.00 1.00

1 2 0.50 -0.75

Polynomial Roots Calculator found no rational roots

Equation at the end of step

3

:

-2x • (2x3 - 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 : -2x = 0

Multiply both sides of the equation by (-1) : 2x = 0

Divide both sides of the equation by 2:

x = 0

Solving a Single Variable Equation:

4.3 Solve : 2x3-1 = 0

Add 1 to both sides of the equation :

2x3 = 1

Divide both sides of the equation by 2:

x3 = 1/2 = 0.500

When two things are equal, their cube roots are equal. Taking the cube root of the two sides of the equation we get:

x = ∛ 1/2

The equation has one real solution

This solution is x = ∛ 0.500 = 0.79370

Two solutions were found :

x = ∛ 0.500 = 0.79370

x = 0