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 transcript:

7-4 Remainder and Factor Theorems

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

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

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

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

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

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

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

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

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

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

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.

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

HW p , 21-27, all odds