polynomial?

Question

Form a polynomial whose zeros and degree are given where a =1

The zeros are -4, 0, 2 and the degree is 3

Answer 1

Create factors for each of the zeroes, and then multiply it out.

y = (x+4) * (x) * (x - 2)

or
y = x^3 + 2x^2 - 8x

Answer 2

I had remembered that x^3, but faltered on what were "zeros." Of course, they are what make a factor zero. Hence, if a zero is -4, what is added to that to make zero is +4. Or, (x+4).

If a zero is zero, then there is nothing to be added to x.

f(x) = (x+4)(x)(x-3) = (x^2+4x)((x-3) = x^3+4x^2-3x^2-12x
f(x) =x^3 +x^2 -12x.

Or y = x^3 +x^2 -12x

Wait, I didn't get the same thing you did, fm. Let's see if I can do this a different way:

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

O.K. I double checked my work. One more time, multiplying in different order, just in case:

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

x^3+x^2 -12x.

Can I get an "Amen!"

Answer 3

if a is a zero then (x-a) is a factor

based on this the polynomial = (x+4)x(x-2)

= x^3 + 2x^2 - 8x

i presume you mean a = 1 means coefficient of x^3 which is one

Answer 4

x(x + 4)(x - 2)
x(x^2 - 2x + 4x - 8)
x(x^2 + 2x - 8)
x^3 + 2x^2 - 8x