Question

8x³+12x²+6x-63
Reslove this into factor​

Answer 1

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