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Warm Up Math III 10/11/12 Find the following using long division:

Warm Up Math III 10/11/12 Find the following using long division:. Remainder Theorem . If a polynomial f(x) is divided by (x-r) and a remainder of R is obtained, then f(r) = R. Example: Use the remainder theorem to find the remainder of the following equation:.

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Warm Up Math III 10/11/12 Find the following using long division:

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  1. Warm Up Math III 10/11/12Find the following using long division:

  2. Remainder Theorem • If a polynomial f(x) is divided by (x-r) and a remainder of R is obtained, then f(r) = R.

  3. Example: Use the remainder theorem to find the remainder of the following equation: Since we are dividing by , we set x – 2 = 0 and solve. Therefore, x = 2. Now, plug

  4. Rational Root Theorem • If a polynomial has rational roots then p is a factor of and is a factor of

  5. Rational Root Theorem • To find the possible roots of a polynomial: • Find all factors of the leading coefficient (called q) • Find all factors of the last term, the one with no variable (called p) • Divided each p by each q.

  6. Example: List all possible rational roots of

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