Answer:(5x+3)(4x2+1)
Explanation:
20x3-12x2+5x-3
Final result :
(4x2 + 1) • (5x - 3)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(((20 • (x3)) - (22•3x2)) + 5x) - 3
Step 2 :
Equation at the end of step 2 :
(((22•5x3) - (22•3x2)) + 5x) - 3
Step 3 :
Checking for a perfect cube :
3.1 20x3-12x2+5x-3 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 20x3-12x2+5x-3
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 5x-3
Group 2: 20x3-12x2
Pull out from each group separately :
Group 1: (5x-3) • (1)
Group 2: (5x-3) • (4x2)
-------------------
Add up the two groups :
(5x-3) • (4x2+1)
Which is the desired factorization
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 4x2+1
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 4 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-1 2 -0.50 2.00
-1 4 -0.25 1.25
1 1 1.00 5.00
1 2 0.50 2.00
1 4 0.25 1.25
Polynomial Roots Calculator found no rational roots
Final result :
(4x2 + 1) • (5x - 3)