Algebra 2 | Unit 2 | Lesson 12: Polynomial Division (Part 1) | Practice Problems

Rewrite \(p(x)\) as the product of linear factors. Draw a rough sketch of the graph of the function.

Tyler thinks he knows one of the linear factors of \(P(x)=x^3-9x^2+23x-15\). After finding that \(P(1)=0\), he suspects that \(x-1\) is a factor of \(P(x)\). Here is the diagram he made to check if he’s right, but he set it up incorrectly. What went wrong?

The polynomial function \(q(x)=2x^4-9x^3-12x^2+29x+30\) has known factors \((x-2)\) and \((x+1)\). Which expression represents \(q(x)\) as the product of linear factors?

• (2x - 5)(x+3)(x-2)(x+1)

• (2x + 3)(x-5)(x-2)(x+1)

• (2x + 15)(x-1)(x-2)(x+1)

• (2x - 15)(x+1)(x-2)(x+1)

Write an expression for the value of the account at the end of three years in terms of the growth factor \(x\). Determine (to the nearest cent) the amount in the account at the end of three years if the interest rate is 4%.

State the degree and end behavior of \(f(x)=5 + 7x - 9x^2 + 4x^3\). Explain or show your reasoning.

Describe the end behavior of \(f(x) = 1 + 7x + 9x^3 + 6x^4 - 2x^5\).

What are the points of intersection between the graphs of the functions \(f(x)=(x+3)(x-1)\) and \(g(x)=(x+1)(x-3)\)?