8x³+12x²+6x-63
Reslove this into factor
Answers
Answer:
8x3-12x2+6x-63
Final result :
8x3 - 12x2 + 6x - 63
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(((8 • (x3)) - (22•3x2)) + 6x) - 63
Step 2 :
Equation at the end of step 2 :
((23x3 - (22•3x2)) + 6x) - 63
Step 3 :
Checking for a perfect cube :
3.1 8x3-12x2+6x-63 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 8x3-12x2+6x-63
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 6x-63
Group 2: -12x2+8x3
Pull out from each group separately :
Group 1: (2x-21) • (3)
Group 2: (2x-3) • (4x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 8x3-12x2+6x-63
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 -63.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4 ,8
of the Trailing Constant : 1 ,3 ,7 ,9 ,21 ,63
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -89.00
-1 2 -0.50 -70.00
-1 4 -0.25 -65.38
-1 8 -0.13 -63.95
-3 1 -3.00 -405.00
Note - For tidiness, printing of 43 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Final result :
8x3 - 12x2 + 6x - 63
Processing ends successfully