Answer:
10x^3 - 7x^5 = x^3(√10 + √7x)(√10 - √7x)
Explanation:
To factor the expression 10x^3 - 7x^5 completely, you can first factor out the greatest common factor, which is x^3. Here's the factored form:
10x^3 - 7x^5 = x^3(10 - 7x^2)
Now, you can further factor the expression inside the parentheses. The expression 10 - 7x^2 is a difference of squares because it can be written as (√10)^2 - (√7x^2)^2. Applying the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), you get:
10 - 7x^2 = (√10 + √7x)(√10 - √7x)
So, the completely factored form of 10x^3 - 7x^5 is:
10x^3 - 7x^5 = x^3(√10 + √7x)(√10 - √7x)
Please note that this expression is fully factored, and you cannot simplify it further without specific numerical values for x and constants.