write f(x) in factored form.
To write a function f(x) in factored form, you need to factorize the expression or equation into its simplest multiplicands. Here's a step-by-step approach:
1. Start with the given function f(x) and make sure it is written in its simplest form.
2. If f(x) is a polynomial, check if it can be factored further. In this case, look for common factors among the terms. For example, if f(x) = 2x^2 + 4x, you can factor out a common factor of 2: f(x) = 2(x^2 + 2x).
3. If f(x) is a quadratic function (in the form of ax^2 + bx + c), try to factorize it using factoring techniques such as:
- Factoring by grouping: If there are four terms, try grouping the terms and factor out common factors. For example, if f(x) = x^2 + 3x + 2, you can rewrite it as (x^2 + x) + (2x + 2) and then factor out common terms: x(x + 1) + 2(x + 1).
- Factoring as a perfect square: If the quadratic expression is in the form of (x + a)^2 or (x - a)^2, it can be factored as (x + a)(x + a) or (x - a)(x - a), respectively.
- Factoring using the quadratic formula: If the quadratic function cannot be easily factored by other methods, you can use the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a to find the roots, and then write the quadratic expression as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots obtained from the formula.
4. If f(x) is a rational function (fraction), check if the numerator and denominator can be factored. In this case, look for common factors and factors that can be canceled out.
5. If f(x) is an exponential or logarithmic function, there might not be a factored form, as they are usually written in their simplest exponential or logarithmic notation.
Remember, not all functions can be easily factored, and sometimes factoring may not be possible. It depends on the nature of the function and the expression involved.