Cubic Function
Factoring
Have to find a factor for the function. Checking if (x-3) is a factor of the function.
Since now it is proven that (x-3) is a factor of the function, the function can be divided by (x-3).
The original function is now partially factored as the quotient is still in quadratic standard form. Now it can be directly factored without long division. And the factors of the original function are:
Factored Formula
Graph
How to get factored form from graph?
By looking at the graph, the factored form can be found. Through finding the x-intercepts on the graph the factors can be found, as x=-1 becomes (x+1). Also by looking at the end behaviors the degree of the function can be found. In the graph above, as x --> negative infinite, y --> negative infinite and as x --> infinite, y --> infinite therefore the leading term is odd and the leading co-efficient is even. To find the "a" value of the factored function, if zero is plugged in for x, the y-intercept (0,-27) can be found. When the graph crosses the x-intercept of if it acts like a linear, quadratic or cubic function that factor will be according. In specific if the curve is flatter rather than more curved, that means that it has a greater exponent.