Question

Write a third-degree polynomial function whose zeros are 1, −3, and 4.

Answer 1

The zeros are 1, −3, and 4, so


x = 1, x = -3, x = 4


x - 1 = 0, x + 3 = 0, x - 4 = 0


(x - 1)(x + 3)(x - 4) = 0


Do you know what the next step is?

Answer 2

im so confused

Answer 3

do you see how I got that so far?

Answer 4

yes

Answer 5

the next step is to expand the left side

Answer 6

we use the distributive property to do that

Answer 7

(x - 1)(x + 3)(x - 4) = 0

(x - 1)[ x(x - 4) + 3(x - 4) ] = 0

(x - 1)[ x^2 - 4x + 3x - 12 ] = 0

(x - 1)( x^2 - x - 12 ) = 0

x( x^2 - x - 12 ) - 1( x^2 - x - 12 ) = 0

x^3 - x^2 - 12x - x^2 + x + 12 = 0

x^3 - 2x^2 - 11x + 12 = 0

Answer 8

So all of that shows you how (x - 1)(x + 3)(x - 4) turns into x^3 - 2x^2 - 11x + 12

Answer 9

im sort of getting it

Answer 10

keep practicing it and I'm sure it'll click more and more

Answer 11

ok

Answer 12

thank you

Answer 13

you're welcome

Answer 14

Is there a polynomial function with any given number of zeros? What is its degree?

Answer 15

what do you mean?

Answer 16

im staring at the question right now trying to understand it myself

Answer 17

oh, if you have 3 zeros, then the degree will be 3

Answer 18

if there were 4 zeros, then the degree is 4

Answer 19

ok thanks

Answer 20

yw