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

Problem

x(−3/2)+2*x(−1/2)+x(1/2)

Solution

1. Identify the term with the lowest exponent to factor out from the expression.

2. Factor out x(−3/2) from each term by subtracting −3/2 from each exponent.

3. Simplify the exponents inside the parentheses.

x(−3/2)*(x0+2*x1+x2)

4. Rewrite the expression inside the parentheses in standard quadratic form.

x(−3/2)*(x2+2*x+1)

5. Recognize that the quadratic x2+2*x+1 is a perfect square trinomial.

6. Factor the perfect square trinomial into (x+1)2

Final Answer

x(−3/2)+2*x(−1/2)+x(1/2)=x(−3/2)*(x+1)2

Want more problems? Check here!