Final answer:
The factored form of the polynomial P(x)=x^5-9x^3 is P(x)= x^3(x-3)(x+3). We get this by taking out the greatest common factor and then using the formula for difference of squares.
Step-by-step explanation:
The given polynomial is P(x)=x^5-9x^3. To factor this polynomial, we first look for the greatest common factor (GCF) of the terms. Here the GCF is x^3. So we factor out x^3 from each term.
So, P(x)=x^3(x^2-9).
Now, look at the polynomial inside the bracket. This is a difference of two squares which can be factored as (a^2-b^2)= (a-b)(a+b). Here a=x and b=3 as x^2=x^2 and 9=3^2.
So, P(x)= x^3(x-3)(x+3). This is the factored form of P(x)=x^5-9x^3.
Learn more about Factoring Polynomials