49y3-1000 factorise explain it
Answers
Answer:
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
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