Question

2. Factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely. Then sketch the graph.

Answer 1

you have to consider the possible rational roots. they will be the positive and negative factors of the constant. then you want to use synthetic division with the factors until you get a remainder of 0. when you find a 0 remainder you know that is a factor. then the numbers left from division make a cubic polynomial. rinse repeat

Answer 2

(x+3)(x+2) = (x^2 + 5x + 6)

Answer 3

are those your two zeros that you have so far?

Answer 4

wait (x+2)(x+3)(x2-4x+6)

Answer 5

that what i got

Answer 6

but i dont know how to graph it

Answer 7

you can factor your quadratic term as well

Answer 8

do you know what the quadratic formula is?

Answer 9

ax2 + bx + c = 0

Answer 10

no here is the quadratic formula
\[\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]

Answer 11

ok

Answer 12

im lost

Answer 13

your quadratic factor. put it into this equation for your last zeros

Answer 14

x^4+x^3-8x^2+6x+36
=x^4 + 2x^3 - x^3 - 2x^2 - 6x^2 -12x + 18x + 36
= x^3(x+2) - x^2(x+2) - 6x(x+2) + 18(x+2)
= (x+2) (x^3 - x^2 - 6x + 18)
= (x+2) (x^3 + 3x^2 - 4x^2 - 12x + 6x + 18)
= (x+2) {x^2(x+3) - 4x(x+3) + 6(x+3)}
= (x+2) (x+3) (x^2-4x+6)

Answer 15

i didnt check any of that. but i will help you with the next step
\[\frac{ 4\pm \sqrt{(-4)^2-4(1)(6)} }{ 2(1) }\]
solve this and you have your next zeros

Answer 16

idk

Answer 17

get as far as you can and ill help you through step by step. you can do the simple arithmatic easily im sure. do you know how to use i yet?

Answer 18

no

Answer 19

first. solve everything under the root. have you gotten that far?

Answer 20

sorry i am not good in math

Answer 21

alight. so (-4)^2 is 16 and -4(6) is -24. so 16-24=-8 correct
so you have
\[\frac{ -4\pm \sqrt{-8} }{ 2 }\]
not you have to use imaginary numbers to get the square root of -8

Answer 22

oh okay

Answer 23

do you know how to simplify radicals?

Answer 24

no but do u time 4 and 8

Answer 25

no you will have
\[\frac{ -4\pm \sqrt{8}i }{ 2 }\]
then you simplify the radical
\[\frac{ -4\pm2\sqrt{2} }{ 2 }\]
then you can factor out a 2 to get rid of the denominator

Answer 26

dont forget the i like i did though

Answer 27

u lost me

Answer 28

hm... if you want to graph it just make a t table and just graph it. wherever the graph crosses the x axis is a zero. i dont think i will be able to explain it much further without further confusing you. unless you want me to give it a shot