Factor 8x3 + 60x2 + 150x + 125Since 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)
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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
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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?
factora 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.polynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).rational expressionsQuotient of two polynomialsP(x)/Q(x)rational root theoremused to find the rational solutions of a polynomial equationrational zero theoremused to find the rational roots of a polynomial function
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