Section 4-3 The Remainder and Factor Theorems. Remainder Theorem Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant,

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Presentation transcript:

Section 4-3 The Remainder and Factor Theorems

Remainder Theorem Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant, P(r), and where Q(x) is a polynomial with degree one less than the degree of P(x).

Example 1

Synthetic Division by x+3 Remainder 13

Divide using synthetic division. By y+2

Divide using synthetic division. By y Remainder of 8

Divide using synthetic division. By (x+2)

Divide using synthetic division. By (x-1)

Divide using synthetic division. By (x+1)

Divide using synthetic division. By (x-4)

Example 3

Example 4

Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x+1)

Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x+4)

Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x-1)

Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x-4)

Example 5