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7-4 Remainder and Factor Theorems. Solve. x 3 + 4x 2 - 15x - 18 = 0 If x - 3 is a factor.

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Presentation on theme: "7-4 Remainder and Factor Theorems. Solve. x 3 + 4x 2 - 15x - 18 = 0 If x - 3 is a factor."— Presentation transcript:

1 7-4 Remainder and Factor Theorems

2 Solve. x 3 + 4x 2 - 15x - 18 = 0 If x - 3 is a factor.

3 Solve. x 3 + 7x 2 + 2x - 40 = 0 If x - 2 is a factor.

4 Solve. x 3 - 2x 2 + 9x - 18 = 0 If x - 2 is a factor.

5 When it is a factor, what can you say about the remainder?

6 Is it a factor? f(x) = x 3 + x 2 + 3x + 3 Is x + 2 a factor?

7 f(x) = x 3 + x 2 + 3x + 3 Find f(-2).

8 f(x) = x 3 + x 2 + 3x + 3 Is x + 3 a factor?

9 f(x) = x 3 + x 2 + 3x + 3 Is x + 1 a factor?

10 Find k such that 2x 4 + x 3 + 5x 2 - 6x + k ÷ x + 2 has a remainder of 5.

11 2x 4 + x 3 + 5x 2 - 6x + k Find k such that x + 2 is a factor.

12 Remainder Theorem (summary) The remainder of f(x) ÷ (x - a) is f(a). Factor Theorem (summary) The binomial (x - a) is a factor of f(x) iff f(a) = 0.

13 f(x) = 3x 4 - 2x 3 + x 2 - 2 f(4) = f(2) =

14 HW p368-369 13-17, 21-27, 31-35 all odds

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