7-4 Remainder and Factor Theorems

Solve.x3 + 4x2 - 15x - 18 = 0If x - 3 is a factor.

Solve.x3 + 7x2 + 2x - 40 = 0If x - 2 is a factor.

Solve.x3 - 2x2 + 9x - 18 = 0If x - 2 is a factor.

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

Is it a factor?

f(x) = x3 + x2 + 3x + 3 Is x + 2 a factor?

f(x) = x3 + x2 + 3x + 3 Find f(-2).

f(x) = x3 + x2 + 3x + 3 Is x + 3 a factor?

f(x) = x3 + x2 + 3x + 3 Is x + 1 a factor?

Find k such that2x4 + x3 + 5x2 - 6x + k ÷ x + 2 has a remainder of 5.

2x4 + x3 + 5x2 - 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) = 3x4 - 2x3 + x2 - 2

f(4) =

f(2) =

HWp368-36913-17, 21-27, 31-35 all odds