# Lesson 11

Finding Intersections

- Let’s think about two polynomials at once.

### Problem 1

What are the points of intersection between the graphs of the functions \(f(x)=x^2(x+1)\) and \(g(x)=x+1\)?

### Problem 2

Select **all** the points of intersection between the graphs of the functions \(f(x)=(x+5)(x-2)\) and \(g(x)=(2x+1)(x-2)\).

\((\text-5, 0)\)

\((\text-\frac12, 0)\)

\((\text-2,\text-12)\)

\((2, 0)\)

\((4, 18)\)

\((5, 30)\)

### Problem 3

What are the solutions to the equation \((x-3)(x+5)=\text-15\)?

### Problem 4

What are the \(x\)-intercepts of the graph of \(y=(5x+7)(2x-1)(x-4)\)?

\(\text-\frac75, \text{-}\frac12, 4\)

\(\frac57, \frac12, 4\)

\(\text{-}\frac75, \frac12, 4\)

\(\frac57, 2, 4\)

### Problem 5

Which polynomial function’s graph is shown here?

\(f(x)=(x+1)(x+2)(x+4)\)

\(f(x)=(x+1)(x-2)(x+4)\)

\(f(x)=(x-1)(x+2)(x-4)\)

\(f(x)=(x-1)(x-2)(x-4)\)

### Problem 6

Draw a rough sketch of the graph of \(g(x)=\text-x^2(x+2)\).

### Problem 7

The graph of a polynomial function \(f\) is shown.

- Is the degree of the polynomial odd or even? Explain how you know.
- What is the constant term of the polynomial?