4.3 The Remainder & Factor Theorems

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Remainder and Factor Theorems

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Presentation transcript:

4.3 The Remainder & Factor Theorems Objective: Find the factors of polynomials using the Remainder & Factor Theorems

P(x)=[x-r] · Q(x) + P(r), Remainder Theorem: If a polynomial P(x) is divided by x-r, the remainder is a constant P(r), and P(x)=[x-r] · Q(x) + P(r), where Q(x) is a polynomial with degree one less than the degree of P(x). Factor Theorem: The binomial x-r is a factor of the polynomial P(x) iff. P(r) = 0. (remainder is 0) Synthetic Division: Shortcut to long division

Ex. 1) Ex. 2) Ex. 3) Use the remainder theorem to find the remainder when x³- x²- 5x- 3 is divided by (x-3). State whether the binomial is a factor of the polynomial. Explain. Ex. 4) Determine the binomial factors of x³- 2x²- 13x- 10

Ex. 5) Find the value of j so that the remainder of (x³+ 6x²- jx- 8) ÷ (x – 2) is 0.