Factoring a cubed function involves expressing it as a product of three linear factors. The general form of a cubed function is ax + bx + cx + d, where a, b, c, and d are constants. To find the factors, we need to identify three numbers that, when multiplied together, give us the coefficient of the x term (a) and, when added together, give us the coefficient of the x term (b). These three numbers are the factors of the coefficient of the x term. Once we have these factors, we can use them to write the function in factored form.
For example, let’s factor the cubed function x – 3x + 2x – 6. The coefficient of the x term is 1, so the factors of 1 are 1 and 1. The coefficient of the x term is -3, so the three numbers that add up to -3 are -1, -2, and 1. We can check that these three numbers indeed satisfy the conditions: (-1) (-2) (1) = 1 and (-1) + (-2) + (1) = -3. Therefore, the factors of the cubed function x – 3x + 2x – 6 are (x – 1)(x – 2)(x + 1).
