The concentration ,in micrograms per milliliter of the antibiotic chloramphenicol is given by 8t^2 -2t^3, in which t is the number of hours after the drug is taken. Factor the polynomial.
To factor the polynomial 8t^2 - 2t^3, we can follow these steps:
Step 1: Rearrange the terms in descending order of exponents:
-2t^3 + 8t^2
Step 2: Look for the greatest common factor (GCF) among the terms. In this case, the GCF is 2t^2:
2t^2(-t + 4)
So, we have factored out 2t^2 from the given polynomial.
Now let's break down the steps to explain how to factor the polynomial:
Explanation:
Step 1: Rearrange the terms in descending order of exponents.
When given a polynomial, it is best to arrange the terms in descending order of exponents. This means that we write the term with the highest power first, followed by the terms with the lower powers. In this case, we have 8t^2 and -2t^3. We rearrange these terms and get:
-2t^3 + 8t^2
Step 2: Look for the greatest common factor (GCF) among the terms.
The GCF is the largest factor that divides evenly into all the terms of the polynomial. In this case, the GCF is 2t^2. To factor this polynomial, we can factor out 2t^2 using the distributive property:
2t^2(-t + 4)
The factor 2t^2 can be pulled out from both terms, leaving us with a common factor and the remaining terms inside the parentheses. This process is called factoring out the GCF.
So, the factored form of the polynomial 8t^2 - 2t^3 is 2t^2(-t + 4).