Lesson 11-2 Remainder & Factor Theorems Objectives Students will: Use synthetic division and the remainder theorem to find P(r) Determine whether a given.

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Remainder and Factor Theorems

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Lesson 11-2 Remainder & Factor Theorems Objectives Students will: Use synthetic division and the remainder theorem to find P(r) Determine whether a given number is a root of P(x) Determine whether x – r is a factor of P(x) and solve P(x) = 0

P(x) = 5x 4 + 4x 3 + 3x 2 + 2x + 1 What is the remainder when P(x) divided by x – 3? Find P(3) Let P(x) = x 3 + x – 10 What is the remainder when P(x) is divided by x + 2? Find P(-2)

Remainder Theorem The function value P(r) = remainder, when P(x) is divided by x - r Factor Theorem If P(r) = 0, then x – r is a factor of P(x), also If x – r is a factor, then P(r) = 0 Using the Theorems If the roots are integers, then they will be factors of a 0 “Factors of the constant (last) term” If we know x – r is a factor, then dividing P(x) by x – r gives other factors

Example 1 P(x) = x 3 – 10x – 75 Is 5 a root?Find P(-2) Example 2 Factor P(x) = x 3 + 3x 2 – 9x + 5 HW 106