Find the zeros of the polynomial function and state the multiplicity of each. f(x) = 3(x + 8)2(x - 8)3

HELP please

\[\large f(x) = 3(x+8)^2(x-8)^3 \]

the zeros are -8 and 8 but no clue what multiplicity is, sorry

When does (x+8) become zero? when does (x-8) become zero?

when x is -8 and 8 so those are the zeros but what is multiplicity?

\[ \large f(x) = 3(x+8)^2(x-8)^3 = 3)x+8)(x+8)(x-8)(x-8)(x-8) \]

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ohh -8 has multiplicity of 2 and 8 has multiplicity of 3?

So (x + 8) becomes zero at x = -8, twice (multiplicity 2) (x-8) becomes zero at x = 8 three times (multiplicity 3).

thank you!

could you help me with another one?

You are welcome.

go ahead.

Find a cubic function with the given zeros. square root of 7, negative square root of 7 , -4

If "a" is a zero, then (x-a) is a factor. If \(\sqrt{7}\) is a factor, then \((x-\sqrt{7})\) is a factor. You are given three zeros and so you have three factors. Multiply them all together to get the cubic function.

In the second line I meant If \(\sqrt{7}\) is a zero, then \((x-\sqrt{7})\) is a factor.

(x-sqr root 7)(x+sqr root 7)(x+4) ?

correct. To multiply the first two make use of the algebraic identity: (x-a)(x+a) = x^2 - a^2 Then multiply that by (x+4)

right ok one second let me solve

x^3+4x^2-7x-28 correct?

Yes, good job.

thank you so much.

You are welcome.

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