[PDF] 5 6 study guide and intervention the remainder and factor theorems

How do you use the factor theorem to find the remainder?

Then use the factor theorem to determine whether x-3 is a factor of f (x) f (x)=2x^3-10x^2+11x+12 Use the remainder theorem to find the remainder when f (x) is divided by x -2. Then use the factor theorem to determine whether x -2 is a factor of f (x) f (x) = 2x^5 + 6x^4 - x^2 - 7x - 12

What is the Chinese Remainder Theorem?

The Chinese remainder theorem (CRT) asserts that there is a unique class a + NZ so that x solves the system (2) if and only if x ? a + NZ, i.e. x ? a (mod N). Thus the system (2) is equivalent to a single congruence modulo N.

How do you find the remainder of a polynomial?

Again, by the Remainder Theorem, f(3) should be the remainder when you divide the polynomial by x - 3. The remainder is 140, so f(3) = 140. Use synthetic substitution to find f(-5) and f (!1 2 )for each function.