To write the form of the partial fraction decomposition, factor the denominator and write the partial fraction decomposition using the factors as denominators.
Step-by-step explanation:
To write the form of the partial fraction decomposition for the given expression, we need to factor the denominator and then determine the partial fractions. First, let's factor the denominator:
x^5 - 7x^4 + 10x^3 = x^3(x^2 - 7x + 10) = x^3(x - 2)(x - 5)
Now, we can write the partial fraction decomposition:
(6x^3 + 4x^2 - 5)/(x^5 - 7x^4 + 10x^3) = A/x + B/x^2 + C/x^3 + D/(x - 2) + E/(x - 5)
where A, B, C, D, and E are constants that we need to solve for.
The probable question can be: The instruction said to write the form of the partial fraction decomposition for (6x^3+4x^2-5)/(x^5-7x^4+10x^3)