Answer:
4x^3-26x^2+15x-3
Step-by-step explanation:
STEP 1:
Simplify 3/1
The equation at the end of step 1:
(4•(x3)-(26•(x2)+15x)-3
STEP 2:
The equation at the end of step 2:
(4 • (x3) - (2•13x2)+ 15x) - 3
STEP 3:
The equation at the end of step 3:
(22x3 - (2•13x2)+ 15x) - 3
STEP 4:
Checking for a perfect cube
4.1 4x3-26x2+15x-3 is not a perfect cube
Trying to factor by pulling out :
4.2 Factoring: 4x3-26x2+15x-3
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 15x-3
Group 2: 4x3-26x2
Pull out from each group separately :
Group 1: (5x-1) • (3)
Group 2: (2x-13) • (2x2)
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 :
4.3 Find roots (zeroes) of : F(x) = 4x3-26x2+15x-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 are 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 4 and the Trailing Constant is -3.
The factor(s) are:
of the Leading Coefficient: 1,2,4
of the Trailing Constant: 1,3
Let us test...
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -48.00
-1 2 -0.50 -17.50
-1 4 -0.25 -8.44
-3 1 -3.00 -390.00
-3 2 -1.50 -97.50
-3 4 -0.75 -30.56
1 1 1.00 -10.00
1 2 0.50 -1.50
1 4 0.25 -0.81
3 1 3.00 -84.00
3 2 1.50 -25.50
3 4 0.75 -4.69
Polynomial Roots Calculator found no rational roots
Final result :
4x3 - 26x2 + 15x - 3
