Question

3. What is a polynomial function in standard form with zeroes 1,2,-3, and -1? the choices are g(x)=x^4 +x^3-7x^2-x+6, x^4 +x^3+7x^2-x+6,x^4 +x^3-7x^2-x-6,and x^4 -x^3-7x^2-x+6

Answer 1

If a polynomial has the given zeroes, then

x = 1
x = 2
x = -3
x = -1

Answer 2

Using algebra, we can re-write the above to say that
x - 1 = 0
x - 2 = 0
x + 3 = 0
x + 1 = 0

Do you understand how I got that?

Answer 3

yea i understand you moved the number over with x

Answer 4

Because after that you'll realize that the expressions on the left are the factors of the function of interest, and by way of the zero product property we can multiply them together

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

Answer 5

so you substitute the zeros for x?

Answer 6

No, you multiply the factors on the right completely.

Answer 7

The factors equal zero when the function equals zero. We don't know yet if the function is g(x)

Answer 8

If it were g(x), then we could set
g(x) = (x - 1)(x - 2)(x + 3)(x + 1)

Answer 9

But we have to multiply the right side first before deciding which expression is correct.

Answer 10

how do you do that?

Answer 11

That depends on how your teacher wants you to do it. If you're doing problems of this type, you are probably expected by your teacher to already understand what it means to multiply factors.

Answer 12

To do multiply them manually, you would just continue to apply multiplication rules for binomials and polymials until you have a completely expanded expression.

Answer 13

And if you were doing it manually, then I believe most people would first multiply (x - 1)(x - 2) then (x + 3)(x + 1)

Answer 14

And then afterwards multiply the products of both together.

Answer 15

@domanboy97 I assume you are multiplying them together?

Answer 16

yes

Answer 17

Let me know what you get

Answer 18

i got my dad to help me and we got x^4 -x^3-7x^2-x+6 is this right?

Answer 19

It's not correct though.

Answer 20

Show me the work you and your dad did to multiply everything out.

Answer 21

We can figure out the mistakes together.

Answer 22

i just did it again and got this x^4 +x^3-7x^2-x+6

Answer 23

I would still like to see the work you did on it.

Answer 24

I would like to see how you multiplied it all together. There are different techniques you can use to do it. I'm trying to see which of them you used.