Michigan Algebra I Sept. 2012

Example 1 In the polynomial, P(x) = x⁴ - 4x³ -2x + 3, how many roots are possible?

There will be a total of 4 roots. How to determine the number of real and non-real roots is a discussion for a later course.

Example 2 How many linear factors can the polynomial, P(x) = x³ - 3x² - 2x + 6, have?

At most, the polynomial will have three linear factors.

*Note: This polynomial can be factored to - three linear factors.