Question

What polynomial has roots of -5, 2, and 4 ? I don't know how to do this at all.

Answer 1

Think about factoring and roots.

(x + Y) = 0 this is how you find roots

for this to work X must equal -Y

Answer 2

Now use the numbers given in the question and substitute each in for X and then figure out what Y must be.

Remember they gave you the roots and you want to find the (x+y) or (x-z).

Answer 3

Okay if I plug the numbers in (-5+y) (2+y) (4+y) would I make then equal zero?

Answer 4

You have three roots so you need three (x +y) factors

They might want to multiply the three factors to come up with the polynomial....

ax^3 + bx^2 + cx + d = 0

Answer 5

ok so -5x^3+2x^2+4xx+d=0

Answer 6

Yes (to answer your question)

(-5+y) = 0 y = ??
(2+y) = 0 y = ??
(4+y) = 0 y = ??

Answer 7

y=5
y=-2
y=-4

Answer 8

Yes and now ...

(x + 5) ( x -2) (x -4) multiply these

Answer 9

is it x^3+40?

Answer 10

No
it will look like this

ax^3 + bx^2 + cx + d = 0

do it parts


(x + 5) ( x -2) = quad then multiply quad and (x -4)

Answer 11

Do the (x + 5) ( x -2) ??

Answer 12

I got fro that one x^2+3x-10

Answer 13

How would I do the other one?

Answer 14

x^2 + 3x - 10 that is what i got

Answer 15

Now just multiply

(x^2 + 3x - 10) (x -4) one term at a time

by that I mean
x^2 times x then 3x times x three -10 times x

then do the same thing only multiply by -4

simplify by collecting the terms

Answer 16

x^2+3x^2+40

Answer 17

No

x^2 times x = x^2 * x^1 = x^? add the exponents

Answer 18

or look at as

x* x* x = x^? remember like with real numbers 2 * 2 * 2 = 8 = 2^3

Answer 19

so it would be x^3+3x^2_____+40???

Answer 20

These are my answer choices
Select one:
A. x^3 - x^2 - 22x + 40
B. x^3 + x^2 - 22x - 40
C. x^3 + 3x^2 - 18x - 40
D. x^3 - 3x^2 - 18x + 40

Answer 21

One more time you need to multiply all three terms by the -4 also

Answer 22

-18

Answer 23

-18x

Answer 24

I need to draw it out so you understand this. I want you to understand the process. I will try to be quick.