Apply the Fundamental Theorem of Algebra

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Notes 6.6 Fundamental Theorem of Algebra

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Apply the Fundamental Theorem of Algebra Notes 5.7 (Day 1) Apply the Fundamental Theorem of Algebra

Fundamental Theorem of Algebra In an equation, the degree is the number of solutions. (Some solutions may have multiplicity.)

Fundamental Theorem of Algebra In a function, the degree is equal to the number of zeros. (Some may be real, and some may be imaginary meaning that this does not guarantee that the function passes through the x axis that many times. You cannot graph an imaginary number on a real number coordinate plane.)

Remember, when talking about equations, they generally do not have zeros, because that term usually refers to functions containing two variables, x and y.

How many solutions does the equation x3 + 5x2 +4x + 20 = 0 have? x4 + 5x2 – 36 = 0 have?

How many zeros does the function f(x) = x4 – 8x3 +18x2 – 27 have? f(x) = x3 + 7x2 + 8x – 16 have?

Find the zeros of the polynomial function.

Find the zeros of the polynomial function.

Find the zeros of the polynomial function.

Homework: P 383 3-8, 10-19