Question

Find the polynomial function with roots 1, 7, and –3 of multiplicity 2.

Answer 1

This is almost the same thing as your last problem. You just need to put in two \((x+3)\) terms. So just multiply out\[(x-1)(x-7)(x+3)(x+3)\]And you will get your polynomial.

Answer 2

so just the x+3 has to be doubled?

Answer 3

correct. Multiplicity is counting how many times you have that root.

Answer 4

but the equation doesnnt single out the x+3

Answer 5

What do you mean?

Answer 6

it says of 1 7 and -3 not just -3

Answer 7

So you want a polynomial with a single root of 1, a single root of 7, and two roots of -3.

Answer 8

ok. so, sofar i have (x^2+7)(x^2+9)

Answer 9

You should be getting \[(x^2-8x+7)(x^2+6x+9)\]

Answer 10

ok do i add them together?

Answer 11

You need to multiply them together again. It's a bit of work, but good practice.

Answer 12

foil?

Answer 13

x^4-14x^3-32x^2+42x-9

Answer 14

You're close, it looks like you just forgot to multiply one or two terms.\[x^4-2x^3-32x^3-30x+63\]

Answer 15

is -2x to the 3rd power?

Answer 16

Yes. Here's a larger version.\[\Large x^4-2x^3-32x^3-30x+63\]

Answer 17

so -34x^3

Answer 18

no...

Answer 19

why not when u have like terms u add them together

Answer 20

I made a typo. Good thing you noticed it. \[\Large x^4-2x^3-32x^2-30x+63\]

Answer 21

lol ok.