Answer: The equation 20x³-25x²+4x-5 can be factored by finding its roots, which are the values of x that make the equation equal to zero.
To find the roots, you can use one of the following methods:
Rational Root Theorem
Synthetic Division
Factor Theorem
Binomial Expansion
I would recommend using the Rational Root Theorem, which states that if a polynomial has a rational root, then it can be expressed as a product of linear factors with rational coefficients.
First, list out the possible rational roots of the equation: ±1, ±2, ±5, ±1/2, ±1/5.
Next, test each root by dividing the equation by (x-root), using synthetic division. If the remainder is zero, then the root is a factor of the equation. Repeat this process until you have found all of the roots.
Finally, factor the equation by grouping the roots into pairs and multiplying each pair to obtain a quadratic factor. Factor each quadratic and simplify the expression.
It is important to note that this is a rather advanced topic in algebra and finding the roots of polynomials can be quite challenging. If you need further assistance, I recommend seeking help from a tutor or textbook on algebra.
Explanation: