Remainder and Factor Theorem Assignment Name: Date: 1.] Thinking; for the moment, about numbers; what are all the factors of 12 {not counting 1 and 12}? 2.] What are the factors of 218+ 23-: 4? 3.] 1li'll'hat are the zeros of 2x1 + 2x 4? 1L] Considering only the factors of the form it k, what is the relationship between the k 1iralues and the zeros? 5.] Make a conjecture [educated guess} for the Factor Theorem: A polynomial fix} has a factor xk if and onlyr if... 5.] Explain why the \"if" direction is true; i.e. why it's true that if flit} has a factor it k, then [The "only if" direction is harder.] I] Now let's use the theorem to factor a polynomial. Use your calculator to nd the zeros of it? 3x2 x + 3 {graph and nd the zeros by eye or use 2nd (SALE zero]. 8.) Once you have found the zeros, what are some factors? (In this case, these are all the factors.) 9.) Let's look at dividing a polynomial by a non-factor. If f(x) = x2 + 7x -5, and you divide by x -2, what is the quotient and remainder? 10.) Notice the 2 in our divisor (x - 2) for #9. What is f(2)? 11.) Make a conjecture for the Remainder Theorem: If a polynomial f(x) is divided by x - k, the remainder is