Answer:
8x3 - 30x + 21
————————
2 • (2x - 3)
Explanation:
Changes made to your input should not affect the solution:
(1): "x3" was replaced by "x^3".
8x3 - 30x + 21
Simplify —————————
4x - 6
Pull out like factors :
4x - 6 = 2 • (2x - 3)
Find roots (zeroes) of : F(x) = 8x3 - 30x + 21
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 8 and the Trailing Constant is 21.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4 ,8
of the Trailing Constant : 1 ,3 ,7 ,21
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 43.00
-1 2 -0.50 35.00
-1 4 -0.25 28.38
-1 8 -0.12 24.73
-3 1 -3.00 -105.00
Note - For tidiness, printing of 27 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Polynomial Long Division
Dividing : 8x3 - 30x + 21
("Dividend")
By : 2x - 3 ("Divisor")
dividend 8x3 - 30x + 21
- divisor * 4x2 8x3 - 12x2
remainder 12x2 - 30x + 21
- divisor * 6x1 12x2 - 18x
remainder - 12x + 21
- divisor * -6x0 - 12x + 18
remainder 3
Quotient : 4x2 + 6x - 6
Remainder : 3
Answer: 8x3 - 30x + 21
————————
2 • (2x - 3)