Question

I need help factoring this and i already know the roots are (x+3) and (x+2)

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

Answer 1

also how do i graph it?

Answer 2

Are you meant to use the remainder and factor theorems?

Answer 3

i do use the remainder but i used synth. div. to get -2,0 and -3,0

Answer 4

If so, then you try the positive and negative multiples of your constant, which would be 36. So your options are: 0, -1, +1, -2, +2, -3, +3 etc.

Answer 5

Well (x+2) is a factor. Then you use -2 in synthetic division and get...

Answer 6

x^3 - x^2 -6x +18

Answer 7

the remainder that would be 0

Answer 8

Repeat the process and you'll find the last root--one must not factor since there are only two roots in the ANS.

Answer 9

If the remainder is 0, you've found a factor.

Answer 10

ok im lost

Answer 11

Have you learned the remainder theorem and the factor theorem?

Answer 12

i learned the remainder theorem the factor theorm i dont know

Answer 13

If you plug a value into a function, f(x), and the y value you calculate is 0, then that point must lie on the x-axis. By definition, you are finding the "factors" of the function in doing so. As well as that, you are finding the x-intercepts.

Answer 14

If your remainder is 0, you have yourself a factor.
The remainder theorem and the factor theorem are said to go hand-in-hand.

Answer 15

@Kinzan i just looked at the lesson again i used synth. div. to get the first 2 points you was saying to find the integers and graph them right? if that is correct then i just need you to walk me trough how to factor it before i use div.

Answer 16

The integers?

Answer 17

Well I used factor theorem. Using positive and negatives of the multiples of the constant of the function, which was 36, and plugged those values into x.

Answer 18

Whichever resulted in a remainder of 0 was a factor.

Answer 19

Use the number of the x-value that resulted in a remainder of 0 in your synthetic division.

Answer 20

ok so after i use foil i should have (x+3) (x+2) (x^2 + 5x + 6) this should be the factored form of the equation?

Answer 21

What are you foiling?

Answer 22

x+3 and x+2 when i use synth div. they become -3 and -2

Answer 23

Sure, okay. Then you used those values to generate the co-efficients for the next steps, right? I'm assuming so.

Answer 24

how do i do that i just tried to graph it and the graph is incorrect

Answer 25

The leading coefficient is positive and the degree is even, so the graph of this function opens upwards, and its end behaviour is similar to a parabola opening upwards.

You have two x-intercepts if you have two roots.

Answer 26

Your y-intercept is (0, 36).

Answer 27

Sketch the graph now, is it correct?

Answer 28

sorry, im still lost here im confused, i already know what the factored form of the problem is how do i get the points on the graph

Answer 29

Your factors are your x-intercepts...you know your y-intercept as well.

Answer 30

factors are -2 and -3 and my y interceps are 0 and 36? i thought the remainder being 0 would be the y-intercept for -2 and -3