Question

use the given zero to find all the zeros of the polynomial function: p(x) = x^4 + x^3 + 9x^2+ 9x
zero: 3i

Answer 1

first of all do the terms in the polynomial have a gcf?

Answer 2

9 or x?

Answer 3

so there is 9 in the x^4?

Answer 4

the gcd of the terms i x since there is x in each term

Answer 5

so the gcf is x well 1 since x isn't a number ?

Answer 6

x is a number

Answer 7

how do i solve it?

Answer 8

\[x^4+x^3+9x^2+9x=x(x^3+x^2+9x+9)\]
First you can factor the x out since each term had an x

Answer 9

now try to factor \[x^3+x^2+9x+9\]
by grouping

Answer 10

What do the first two terms have in common?

Answer 11

exponents

Answer 12

well the variable x

Answer 13

so the only thing x^3 and x^2 have in common is x?

Answer 14

you wouldn't be able to factor anymore out of x^3+x^2 then just x?

Answer 15

what else would there be to factor?

Answer 16

what about x^2

Answer 17

ok so x^2