Question

factor f(x) into linear factors given that k is a zero of f(x): f(x)=x^4+3x^3-12x^2-52x-48; k= -2 (multiplicity of 2) alright I know how to factor that out, but..... what is -2 multiplicity of 2?

Answer 1

it means that k is a double zero.

Answer 2

ie f(x)=(x+2)^2*p(x)

Answer 3

I am so lost k is a double zero? what does that do to the factoring of -2 then?

Answer 4

have you learned polynomial division yet?

Answer 5

yes we have but no where in my notes book anything can I find reference to multiplicity of the k value

Answer 6

the k value of 2 means that k is a zero both of f(x) and of f(k)/(x-k)

Answer 7

for example, the polynomial x^2+2x+1 has a zero k=-1 with multiplicity 2

Answer 8

since it can be written as (x+1)^2.

Answer 9

when everything is factored out I come up with f(x)=(x+2)(x^3+x^2-14x-24 does that seem right?

Answer 10

yes. now divide x^3+x^2-14x-24 by x+2 again.

Answer 11

x^2-x-12?
Thank you soooooooooo much

Answer 12

;)

Answer 13

also don't forget to factor that

Answer 14

into (x+3)(x-4)