divide 2x ^5-3x^2-3 by x^2-1
please answer fast urgent
Answers
Answer:2x3 - 3
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
STEP
2
:
Equation at the end of step
2
:
STEP
3
:
2x5 - 3x2
Simplify —————————
x2
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2x5 - 3x2 = x2 • (2x3 - 3)
Trying to factor as a Difference of Cubes:
4.2 Factoring: 2x3 - 3
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 :
4.3 Find roots (zeroes) of : F(x) = 2x3 - 3
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 integershe 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 -3.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1 ,3
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -5.00
-1 2 -0.50 -3.25
-3 1 -3.00 -57.00
-3 2 -1.50 -9.75
1 1 1.00 -1.00
1 2 0.50 -2.75
3 1 3.00 51.00
3 2 1.50 3.75
Polynomial Roots Calculator found no rational roots
Canceling Out :
4.4 Canceling out x2 as it appears on both sides of the fraction line
Trying to factor as a Difference of Cubes:
4.5 Factoring: 2x3 - 3
Check : 2 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Final result :
2x3 - 3