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

Question

The zeros are -4, 0, 2 and the degree is 3.
This is not my assignment nor a test, i just wanna know how to get the right answer because im totally confused. Thanks.

Answer 1

given the zeroes of y:
if x = -4, 0 or 2, then y = 0. Therefore it passes through
(-4, 0)
(0,0)
(2,0)

In other words -4, 0 and 2 are x-intercepts of the polynomial.

The polynomial (3rd degree) can be expressed as:
y = x³ + ax² + bx + c
It can also be expressed as
y = (x - x1)(x - x2)(x - x3)
where n is a constant.

When you substitute x1 to the expression
y = (x1 - x1)(x1 - x2)(x1 - x3)
y = (0)(x1 - x2)(x1 - x3)
y = 0

Therefore, x1 is a zero

The same goes with x2 and x3. Therefore you can put the zeroes into our expression

y = (x - (-4))(x - 0)(x - 2)
y = (x + 4)(x)(x - 2)
y = x(x + 4)(x - 2)
or
y = x(x² + 2x - 8)
y = x³ + 2x² - 8x

That is your 3rd degree polynomial! Hope this helps^_^

Answer 2

If x = -4, x = 0, and x = 2, then x+4, x-2, and x-0 (or just x) are factors of the polynomial. Multiply these factors together to get your polynomial:

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

x(x^2+2x-8) =

x^3+2x^2-8x

Answer 3

utilising the words that must be 0, use: (x + 3) * (x - 3) * (x - a million) = 0 while x = -3, 3, and a million Now merely multiply mutually: (x^2 - 9) * (x - a million) x^3 - x^2 - 9x + 9 has ultimate coefficient a million and degree 3. for that reason: x^3 - x^2 - 9x + 9 is the answer.