Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.

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Presentation transcript:

Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division

You will be able to used the remainder theorem and rational roots theorem. If a polynomial f(x) is divided by (x – a) then the remainder is equal to f(a). If the remainder is 0 then (x – a) is a factor of the polynomial. Let f(x) = x 4 – 6x 3 + 8x 2 + 5x + 13, evaluate f(4). Use Direct Substitution. Use Synthetic Division (The answer is the remainder) Is (x – 4) a factor?

Is (x – 3) a factor of x 3 + 5x 2 – 12x – 36? Factor Theorem (x – a) is a factor of f(x), if f(a) = 0 Page 187 The rational roots theorem states that every rational zero is equal to p/q, where p is a factor of the constant and q is a factor of the leading coefficient. What are the possible roots of f(x) = 5x 3 - 6x 2 – 9x + 2? Factors of p are Factors of q are

Determine the zeros of f(x) = 5x 3 - 6x 2 –9x + 2? The possible rational roots were

When a polynomial is divided by x – a, where a>0, if all terms of the quotient and the remainder are positive then a is an upper bound. When a polynomial is divided by x – a, where a<0, if all terms of the quotient and remainder alternate in sign then a is a lower bound. Consider the function p(x) = 2x 3 – 11x 2 – 10x + 55 Is 7 an upper bound? Is -3 a lower bound?

Exit Explain how the theorems allow you to determine the zeros without graphing? Page 193 #56 ACT: If x 2 + 6x + 8 = x, then x equals which of the following? A) -2B) -1C) 0D) 1E) 2