Factor

Problem

(x2+2)(5/2)+2*x*(x2+2)(3/2)+x2√(,x2+2)

Solution

1. Rewrite the square root term using a fractional exponent to make the expression consistent.

(x2+2)(5/2)+2*x*(x2+2)(3/2)+x2*(x2+2)(1/2)

2. Identify the greatest common factor among the terms, which is the base (x2+2) raised to the lowest power present in the expression.

GCF=(x2+2)(1/2)

3. Factor out the GCF from each term by subtracting the exponent 1/2 from the exponents of each term.

(x2+2)(1/2)*((x2+2)2+2*x*(x2+2)1+x2)

4. Recognize the expression inside the parentheses as a perfect square trinomial of the form a2+2*a*b+b2 where a=(x2+2) and b=x

a2+2*a*b+b2=(a+b)2

5. Substitute the values of a and b into the perfect square formula.

(x2+2)(1/2)*((x2+2)+x)2

6. Simplify the expression inside the squared term.

(x2+2)(1/2)*(x2+x+2)2

Final Answer

(x2+2)(5/2)+2*x*(x2+2)(3/2)+x2√(,x2+2)=(x2+2)(1/2)*(x2+x+2)2

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