Question

find a polynomial of the specific degree that has the given zeros

Answer 1

Degree 3; zeros -1,1,3

Answer 2

For each zero, a, there is a binomial x - a.
Multiply all three binomials together to find the polynomial.

Answer 3

Well you know that when you factor out a polynomial you get something that looks like

(x + ...) ( x - ...) ( x - ...) etc...

Well this would be the factorization of a 3rd degree polynomial...

With the given zeros...all you do is plug those in next to the 'x'

(x + 1)(x - 1)(x - 3)

You may have noticed that I switched the signs of your zeros (ie changed -1 to 1 and 3 to -3...this is because your number are what you plug in above to make that equation = 0...

So if you plugged in 3 into the equation above you have

(3 + 1)(3 - 1)(3 - 3) = 0 right?

So now all you do ...is multiply it out...

(x + 1)(x - 1)(x - 3) multiplied out = ?

Answer 4

x^3-3x-x+3
thanks!
I should've known that >.<

Answer 5

I'm sure you meant -3x^2 for the second term.

Answer 6

how come?

Answer 7

is it because the first degree is 3, then the next powers gets reduced?

Answer 8

x^3-3x^2-x+3
degree 3--2--1--0

Answer 9

You wrote:

\(x^3-3x-x+3\)

Answer is:

\(x^3-3x\color{red}{^2}-x+3\)

You left out the exponent 2 from the second term.

Answer 10

Not necessarily @Powerful22 an exponent can be canceled (what if something came up to a 0?)

(x + 1)(x - 1) = x^2 - 1

(x^2 - 1)(x - 3) = x^3 - 3x^2 - x + 3

Just doing the x^2 times the -3 in that one gives you the 3x^2

Answer 11

(x + 1)(x - 1)(x - 3) =
= (x^2 - 1)(x - 3) (Using the product of a sum and a difference.)
= x^3 - 3x^2 - x + 3 (Using FOIL)

Answer 12

oh ya ya
thanks again to both of you @mathstudent55 and @johnweldon1993
You are truly are life savors <333

Answer 13

ou're welcome.Y

Answer 14

No problem!

Answer 15

that was a great idea, multiplying the first factors and then multiply it by the third factors sounds comprehensible! :D