ANSWER:

Step by Step Solution:

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "Y3" was replaced by "y^3".

STEP

1

:

Equation at the end of step 1

72y3 - 1000

STEP

2

:

Trying to factor as a Difference of Cubes

2.1 Factoring: 49y3-1000

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 : 49 is not a cube !!

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

Polynomial Roots Calculator :

2.2 Find roots (zeroes) of : F(y) = 49y3-1000

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

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers y 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 49 and the Trailing Constant is -1000.

The factor(s) are:

of the Leading Coefficient : 1,7 ,49

of the Trailing Constant : 1 ,2 ,4 ,5 ,8 ,10 ,20 ,25 ,40 ,50 , etc

Let us test ....

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

-1 1 -1.00 -1049.00

-1 7 -0.14 -1000.14

-1 49 -0.02 -1000.00

-2 1 -2.00 -1392.00

-2 7 -0.29 -1001.14

Note - For tidiness, printing of 55 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

49y3 - 1000