Investigate graphical and algebraic representations of a polynomial function and its linear factors.

• Students will discover that the zeros of the linear factors are the zeros of the polynomial function.
• Students will discover that the real zeros of a polynomial function are the zeros of its linear factors.
• Students will determine the linear factors of a quadratic function.
• Students will connect the algebraic representation to the geometric representation.
• Students will see the effects of a double and/or triple root on the graph of a cubic function.
• Students will see the effects of the leading coefficient on a cubic function.
• Students will look for and make use of structure (CCSS Mathematical Practice).
• Students will look for and express regularity in repeated reasoning (CCSS Mathematical Practice).

• Zeros
• Double or triple root
• Leading coefficient

This lesson merges graphical and algebraic representations of a polynomial function and its linear factors.

As a result, students will:

• Manipulate the parameters of the linear functions and observe the resulting changes in the polynomial function.
• Find the zeros of the polynomial equations by finding the zeros of the linear factors.