| 8x3 + 22x2 - 6x | |
| 4x - 1 |
We do this by factoring numerator and denominator separately first
Factor 8x3 + 22x2 - 6x
Evaluating the expression you entered
Factor out a term of 2x
Factor out 2x from 8x3
Our new constant becomes 8 ÷ 2 = 4
Our new x variable piece becomes
x(3 - 1) = x2
Our new term becomes 4x2
Factor out 2x from 22x2
Our new constant becomes 22 ÷ 2 = 11
Our new x variable piece becomes
x(2 - 1) = x1
Our new term becomes 11x
Factor out 2x from -6x
Our new constant becomes -6 ÷ 2 = -3
Our new x variable piece becomes
x(1 - 1) = x0 = 1
Our new term becomes -3
Our factored expression is:
2x(4x2 + 11x-3)Attach our factored out piece from the beginning of our calculation for our final expression:
2x(4x2 + 11x - 3)Factor 4x - 1
Our factored out term becomes:
Our factored rational expression is as follows:
| 2x(4x2 + 11x - 3) | |
| (4x - 1) |
(4x - 1)
Common Core State Standards In This Lesson
HSA.SSE.A.2, HSA.APR.B.3
What is the Answer?
(4x - 1)
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.
* 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)
a3 + b3 = (a + b) (a2 - ab + b2)
a3 - b3 = (a - b) (a2 + ab + b2)
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
