Illustrative Math - Algebra 2 - Unit 2 - Lesson 14

Mai graphs a polynomial function, f(x), that has three linear factors (x+6), (x+2), and (x-1). But she makes a mistake. What is her mistake?

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Here is the graph of a polynomial function with degree 4. Select all of the statements that are true about the function.

• The leading coefficient is positive.
• The constant term is negative.
• It has 2 relative maximums.
• It has 4 linear factors.
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State the degree and end behavior of f(x)=2x^{3}-3x^{5}-x^{2}+1. Explain or show your reasoning.

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Is this the graph of g(x)=(x-1)^{2}(x+2) or h(x)=(x-1)(x+2)^{2}? Explain how you know.

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Kiran thinks he knows one of the linear factors of P(x)=x^{3}+x^{2}-17x+15. After finding that P(3)=0, Kiran suspects that x-3 is a factor of P(x), so he sets up a diagram to check. Here is the diagram he made to check his reasoning, but he set it up incorrectly. What went wrong?

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The polynomial function B(x)=x^{3}+8x^{2}+5x-14 has a known factor of (x+2). Rewrite B(x) as a product of linear factors.

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