Remainder & Factor Theorems

Exercises for students:
Solve the following problems on paper and check your working using the above applet:
(1) Find the remainder when x³ - 2x² - 5x + 6 is divided by x + 1
(2) Find the remainder when x³ - 2x² - 5x + 6 is divided by x - 2
(3) Show that (x + 2) is a factor of x³ - 2x² - 5x + 6
(3) Show that (x - 3) is a factor of x³ - 2x² - 5x + 6





Summary

Let f(x) be a polynomial in x.
Remainder Theorem: The remainder when f(x) is divided by (x - a) is f(a).
Factor Theorem: If f(a) = 0, then (x - a) is a factor of f(x).





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