Algebta (factoring polynomials)

[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.

 

[OrbitalPower]

I figured it out. Get CD and factor - just thought i was missing some rule or something.

 

[Architeuthis Dux]

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!