Algebta (factoring polynomials)

  • Thread starter OrbitalPower
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In summary, algebraic factoring is the process of breaking down a polynomial expression into simpler, smaller expressions. This technique is useful in solving equations, simplifying expressions, and finding roots. The most common methods of factoring include the greatest common factor, grouping, difference of squares, and trinomial factoring. With practice and understanding of key concepts, factoring polynomials can be a powerful tool in solving complex problems in algebra.
  • #1
OrbitalPower
[SOLVED] Algebta (factoring polynomials)

Homework Statement



x^2 * [ (1/2) * (1-x^2)^(-1/2) * (-2x)] + (1 - x^2)^(1/2) * (2x)

factor this down.


Homework Equations


n/a


The Attempt at a Solution



-x^3*(1- x^2)^(-1/2) + 2x(1 - x^2)^(1/2)

I understand how you get to this part, but I can't get to:

x * (2 - 3x^2)/ (sqrt(1 - x^2))

after trying factoring by substitution etc.
 
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  • #2
I figured it out. Get CD and factor - just thought i was missing some rule or something.
 
  • #3


Great job on solving the problem and getting to the correct expression! Factoring polynomials can be a challenging but important skill in mathematics. In this case, we can use the distributive property to factor out a common factor of x from both terms in the expression. This will give us:

x * [(-x^2 * (1 - x^2)^(-1/2)) + (2 * (1 - x^2)^(1/2))]

Next, we can simplify the inside of the brackets by using the power rule for exponents. This will give us:

x * [(-x^2 * (1 - x^2)^(-1/2)) + (2 * (1 - x^2)^(1/2))]

= x * [(-x^2 * (1 - x^2)^(-1/2)) + (2 * (1 - x^2)^(1/2))]

= x * [(2 - 3x^2)/ (sqrt(1 - x^2))]

Thus, the final factored form is x * (2 - 3x^2)/ (sqrt(1 - x^2)). Keep up the good work in your algebra studies!
 

Related to Algebta (factoring polynomials)

What is algebra?

Algebra is a branch of mathematics that deals with the manipulation of symbols and equations to solve problems.

What are polynomials?

Polynomials are expressions that consist of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and division.

What is factoring in algebra?

Factoring in algebra is the process of breaking down a polynomial into smaller factors that can be multiplied together to obtain the original polynomial.

Why is factoring important?

Factoring is important because it allows us to simplify complex expressions and solve equations more easily. It is also a fundamental concept in algebra and is used in many real-life applications.

What are the different methods of factoring polynomials?

The most common methods of factoring polynomials are greatest common factor (GCF), difference of squares, trinomial factoring, and grouping. Other methods include factoring by grouping and factoring by trial and error.

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