Lesson 11-2Remainder & Factor Theorems

ObjectivesStudents 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) = 5x4 + 4x3 + 3x2 + 2x + 1

What is the remainder when P(x) divided by x – 3?

Find P(3)

Let P(x) = x3 + 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 a0

“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) = x3 – 10x – 75

Is 5 a root? Find P(-2)

Example 2 Factor P(x) = x3 + 3x2 – 9x + 5

HW 106