Question

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

Answer 1

HELP please

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

lucky guy you are! You have the best possible people watching/helping you!

Answer 8

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

Answer 9

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

Answer 10

thank you!

Answer 11

could you help me with another one?

Answer 12

You are welcome.

Answer 13

go ahead.

Answer 14

Find a cubic function with the given zeros.

square root of 7, negative square root of 7 , -4

Answer 15

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.

Answer 16

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

Answer 17

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

?

Answer 18

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)

Answer 19

right ok one second let me solve

Answer 20

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

correct?

Answer 21

Yes, good job.

Answer 22

thank you so much.

Answer 23

You are welcome.