Question 1068849
Options b) and c) show polynomials of degree 3:
b) y= 2(x+3)^2(x-5) an
c) y= 4(x+3)(x-5)(x+15)
Polynomials of degree 3 can be called "cubic functions,"
but the name "quadratic" is reserved for polynomial of degree 2,
like choices a) and d) :
a) y= -1/2(x+3)(x-5)
d) y=(x+5)(x-3) 
 
If a polynomial function has a {{{5}}} as a zero,
its factored form will have the factor {{{(x-5)}}} .
If a polynomial function has a {{{-3}}} as a zero,
its factored form will have the factor {{{(x-(-3))=(x+3)}}} .
Substituting {{{x=5}}} in a polynomial with {{{(x-5)}}} as a factor will make the polynomial zero.
Substituting {{{x=-3}}} in a polynomial with {{{(x+3)}}} as a factor will make the polynomial zero.
{{{highlight(matrix(1,2,"a )",y= (-1/2)(x+3)(x-5)))}}} is
a quadratic function,
and it has {{{-3}}} and {{{5}}} as zeros.


A polynomial is not allowed to have more zeros than its grade.
A polynomial of degree 2,
such as {{{y=(x+5)(x-3)}}} ,
can have at most 2 zeros.
Substituting {{{x=-5}}} or {{{x=3}}} in {{{y=(x+5)(x-3)}}}
gives you {{{y=0}}} ,
so obviously the zeros of {{{y=(x+5)(x-3)}}}
are {{{3}}} and {{{-5}}} .