Given the polynomial
Use the Remainder Theorem to determine
Divide the polynomial by
. What is the remainder?
Now use the Factor Theorem to determine one factor of
. (See the Math Notes box in this lesson.)
is the zero of the function. What is the corresponding factor?
Use your answer to part (b) to determine another factor.
Try using an area model. A 2 by 3 rectangle, labeled as follows: left edge, x, minus 2, interior top, left, x, cubed.
Labels added: top edge, left, x, squared, interior bottom, left, negative 2, x, squared, interior top, middle, negative 4, x squared.
Labels added: top edge, middle, negative 4, x, interior bottom, middle, 8, x, interior top, right, negative x.
Labels added: top edge, right, negative 1, interior bottom, right, 2.
What are all the solutions of
See part (a) for one solution.
Use the Quadratic Formula to find the solutions to