Since we have 4 terms, note the following Cube root calculations:
The Cube root of the first term 8x3 is denoted below:Cube Root of the Constant Piece = (8)1/3 = 2
Cube Root of the Variable Piece (Divide exponents by 3) = x3÷3 = x
Our final Cube root term becomes 2x
The Cube root of term 4 = 125 is denoted below:
Cube Root of the Constant Piece = (150)1/3 = 5
Our final Cube root term becomes 5
8x3 + 60x2 + 150x + 125 fits a pattern which is called a binomial expansion.
The binomial theorem is shown below:
The formula for this is a(x + y)n = aΣ[k = 0 to n]C(n,k) xn-kyk where| C(n,k) = | n! |
| k!(n - k)! |
In this case, n = 3, x = 2x, a = < b > < span style='color:green' > < /span > < /b > , and y = 5 and our factored expression becomes:
(2x + 5)3
To prove this, we check our expand calculator
Our factored out term becomes:
((2x + 5)3)
You have 1 free calculations remaining
What is the Answer?
((2x + 5)3)
How does the Factoring and Root Finding Calculator work?
Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:
* Difference of Squares
* Sum of Cubes
* Difference of Cubes
* Binomial Expansions
* Quadratics
* Factor by Grouping
* Common Term
This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots
* Factors and simplifies Rational Expressions of one fraction
* Determines the number of potential positive and negative roots using Descarte’s Rule of Signs
This calculator has 1 input.
What 3 formulas are used for the Factoring and Root Finding Calculator?
a2 - b2 = (a + b)(a - b)a3 + b3 = (a + b) (a2 - ab + b2)
a3 - b3 = (a - b) (a2 + ab + b2)
For more math formulas, check out our Formula Dossier
What 5 concepts are covered in the Factoring and Root Finding Calculator?
- factor
- a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- rational expressions
- Quotient of two polynomials
P(x)/Q(x) - rational root theorem
- used to find the rational solutions of a polynomial equation
- rational zero theorem
- used to find the rational roots of a polynomial function
