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Published byJeremy Watson Modified over 6 years ago

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Linear Factorizations Sec. 2.6b

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First, remind me of the definition of a linear factorization… f (x) = a(x – z )(x – z )…(x – z ) An equation in the following form: 12n

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Now, Our Practice Problems: Find all zeros of the given function, and write the function in its linear factorization. Check the graph for possible real zeros… Possibly, x = –2, x = 1, and x = 4 –21–3–55–68 –210–1010–8 1–55 40 Check and factor, using synthetic division:

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Now, Our Practice Problems: Find all zeros of the given function, and write the function in its linear factorization. 11–55 4 1–41 1 1 0

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Now, Our Practice Problems: Find all zeros of the given function, and write the function in its linear factorization. 41–41 404 1010

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Now, Our Practice Problems: Find all zeros of the given function, and write the function in its linear factorization. Complete Linear Factorization:

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Now, Our Practice Problems: The complex number z = 1 – 2i is a zero of the given function. Find the remaining zeros of the function, and write it in its linear factorization. 1 – 2i40171465 4 – 8i–12 – 16i–27 – 26i–65 45 – 16i–13 – 26i04 – 8i

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Now, Our Practice Problems: The complex number z = 1 – 2i is a zero of the given function. Find the remaining zeros of the function, and write it in its linear factorization. 1 + 2i44 – 8i5 – 16i–13 – 26i 4 + 8i8 + 16i13 + 26i 41308 Use the quadratic formula to find the last two zeros… 1 + 2i must also be a zero!!!

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Now, Our Practice Problems: The complex number z = 1 – 2i is a zero of the given function. Find the remaining zeros of the function, and write it in its linear factorization. Now we can write the linear factorization…

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Now, Our Practice Problems: The complex number z = 1 – 2i is a zero of the given function. Find the remaining zeros of the function, and write it in its linear factorization.

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