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**5.5: Polynomial Long Division and Synthetic Division**

Academy Algebra II 5.5: Polynomial Long Division and Synthetic Division HW: 5.4: p.357 (30-40 even, even)

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Divide

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**Polynomial Long Division vs. Synthetic Division**

Polynomial Long Division can be used for any two polynomials. Synthetic Division: the divisor has to be in the form x – k, where k is any constant.

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**Divide using polynomial long division:**

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**Divide using synthetic division:**

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Divide:

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Divide:

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Divide:

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**5.5: Given polynomial f(x) and a factor of f(x), factor f(x) completely.**

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**5.5: FINISH: Polynomial Long Division and Synthetic Division**

Academy Algebra II 5.5: FINISH: Polynomial Long Division and Synthetic Division Hw: 5.5: p.366 (8, 22, 28, 30, 32, 36)

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**Given polynomial f(x) and a factor of f(x), factor f(x) completely.**

Steps 1.) Divide the polynomial and the factor. 2.) Factor the answer. 3.) Write out all factors.

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**Given polynomial f(x) and a factor of f(x), factor f(x) completely.**

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**Given polynomial f(x) and a zero of f(x), find the other zeros.**

Zeros: answers to the polynomial equation f(x) = 0. Process. 1.) Use the zero to factor the polynomial completely. 2.) Solve to find the other zeros.

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**Given polynomial f(x) and a zero of f(x), find the other zeros.**

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**Given polynomial f(x) and a zero of f(x), find the other zeros.**

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**Given polynomial f(x) and a factor of f(x), factor f(x) completely.**

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**Given polynomial f(x) and a zero of f(x), find the other zeros.**

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**Academy Algebra II 5.6: Find Rational Zeros**

HW tonight: p.374 (4-10 even) Tomorrow: p.374 (14-20 even) Next day: p (24-30 even)

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**List all possible rational zeros using the rational zero theorem.**

Every rational zero of a function has the following form:

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**List all possible rational zeros using the rational zero theorem.**

Example: List the possible rational zeros for the function: Factors of the constant: Factors of the leading coefficient: Possible rational zeros: Possible rational zeros:

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**List all possible rational zeros using the rational zero theorem.**

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**List all possible rational zeros using the rational zero theorem.**

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**Find the zeros of a polynomial function.**

List the possible rational zeros of the function. Test the zeros using division. (Since the zeros are x-intercepts, when you divide you should end up with a remainder of zero.) Graph the function in the calculator to narrow your list. Only check reasonable values from the list. The number of zeros is the same as the degree of the polynomial.

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**Find all real zeros of the function.**

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**Do Now: Find all real zeros of the function.**

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**(Calculator and no calculator section)**

Academy Algebra II 5.6: Find Rational Zeros HW tonight: p.374 (16-26 even) Quiz Friday: 5.5, 5.6 (Calculator and no calculator section)

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**Find all real zeros of the function.**

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**Find all real zeros of the function.**

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**Do Now: Find all real zeros of the function.**

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EXAMPLE 2 Find all real zeros of f (x) = x 3 – 8x 2 +11x + 20. SOLUTION List the possible rational zeros. The leading coefficient is 1 and the constant.

EXAMPLE 2 Find all real zeros of f (x) = x 3 – 8x 2 +11x + 20. SOLUTION List the possible rational zeros. The leading coefficient is 1 and the constant.

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