factor this
6e^4s^5-2r^2s^3+14r^3s^4
r^4-11r^3+24r^2
To factor the given expressions, let's start with the first expression:
6e^4s^5 - 2r^2s^3 + 14r^3s^4
First, observe that each term has a common factor of s^3. We can factor it out:
s^3(6e^4s^2 - 2r^2 + 14r^3s)
Next, let's focus on the expression inside the parentheses:
6e^4s^2 - 2r^2 + 14r^3s
There is no common factor among the three terms, so we need to look for other ways to factor it. There is a common factor of 2 in the last two terms, which we can factor out:
2(3e^4s^2 - r^2 + 7r^3s)
Now, we need to further factor the expression inside the parentheses:
3e^4s^2 - r^2 + 7r^3s
At this point, we cannot factor this expression any further, so the complete factored form of the first expression is:
s^3 * 2 * (3e^4s^2 - r^2 + 7r^3s)
Moving on to the second expression:
r^4 - 11r^3 + 24r^2
We can find the factors by factoring out the greatest common factor, if there is one. Here, there is a common factor of r^2:
r^2(r^2 - 11r + 24)
Next, let's factor the expression inside the parentheses:
r^2(r - 8)(r - 3)
So, the complete factored form of the second expression is:
r^2 * (r - 8) * (r - 3)
To summarize:
The factored form of the first expression is: s^3 * 2 * (3e^4s^2 - r^2 + 7r^3s)
The factored form of the second expression is: r^2 * (r - 8) * (r - 3)