The expression x-a is a factor of a polynomial if and only if the value a is a zero of the related polynomial function.
We know that - 1, - 2, - 3, and - 4 are zeros of our function. Therefore, we can write our polynomial function as the product of four factors.
y = ( x-( - 1) ) ( x-( - 2) ) ( x-(- 3) ) ( x-(- 4) )
⇕
y=(x+1)(x+2)(x+3)(x+4)
Finally, we can apply the Distributive Property to express the function in standard form.
We can check our answer by substituting the given zeros for x. If the result is y=0, it means that the given numbers are actually zeros of the function and our answer is correct. Let's start by checking - 1.
