Please describe and show it in a different example:

1. Create TWO Polynomial Functions with the following conditions:

• A linear function, h(x), and a degree 4 polynomial function, P(x).
• The leading coefficient of P(x) can NOT be |1|, the -intercept of both graphs can NOT be 0. h(x) can not be a horizontal nor vertical line.
• One of the factors of P(x) must be repeated 2 times, one of the zeros of P(x) must be a fraction. The zeros should have a mix of positive and negative numbers.
• P(x) and h(x) intersect with each other, and there are at least two points of intersections (POls), which x-coordinates of those two of the POls must be integers/fractions. The POls CAN NOT be on the x-axis.

2. HANDWRITTEN REPORT: Your report will include the following:

• State h(x) and P(x) in standard form.
• Step-by-step how-to factor P(x), you need to state the correct theorem(s) to support your work.
• Determine all features needed to graph P(x). Show all your work.
• A well-labelled graph, by hand or using a graphing tool, that contains both h(x) and P(x) within the same axes. Show intersections of the graphs clearly.
• Determine the intervals when h(x) P(x), algebraically. Show all your work. Check your work using the graph from Desmos.
• Based on the graph, indicate the intervals of increase and decrease.