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Home > INT3 > Chapter 8 > Lesson 8.3.2 > Problem 8-112


Carlo is trying to factor the polynomial to determine all of its zeros. He discovers one factor by making a guess and dividing the polynomial, so he has . Now he is trying to factor , so he tries dividing it by then by , and finally by , but none works without a remainder. Then Teo comes by and says, “You should look at the graph.”

  1. How does the graph help?

    It shows that is a double root, so is a repeated factor.

  2. Complete the problem.

    Divide by 2 by 3 rectangle, labeled as follows: left edge, x, minus 3, top edge, left, x, squared, interior top, left, x squared.

    Labels added: Interior bottom, left, negative 3, x, squared, interior top, middle, 2, x squared.

    Labels added: top edge, middle, 2, x, interior bottom, middle, negative 6, x, interior top, right, negative x.

    Labels added: top edge, right, negative 1, interior bottom, right, 3.

    Now use the Quadratic Formula to solve for .

Continuous, curved graph, Decreasing from top left, turning at the following approximate points: low vertices: (negative 1.5, comma negative 35), & (3, comma 0), & high vertex, (1, comma 10), with x intercepts, at 3, & between negative 3 & negative 2, & between 0 & 1.