Which polynomial function has x-intercepts –2, 0, and 1 and passes through the point (2, 16)?
A). f(x)=x^3-x^2+2x
B). f(x)=x^3+x^2-2x
C). f(x)=2x^3-2x^2+2x
D). f(x)=2x^3+2x^2-4x

Question

Which polynomial function has x-intercepts –2, 0, and 1 and passes through the point (2, 16)?
A). f(x)=x^3-x^2+2x
B). f(x)=x^3+x^2-2x
C). f(x)=2x^3-2x^2+2x
D). f(x)=2x^3+2x^2-4x

campbell_st · Answer

well the x intercepts are the zeros

so if   x = -2   is a zero, then (x + 2) is a factor
          x = 0   is a zero   then x is a factor 
          x = 1 is a zero then (x - 1) is a factor

so the polynomial is 

y= ax(x +2)(x-1)

where a is a constant... 

substitute the value from the point x = 2 and y = 16 to find a. 

the just distribute for the answer

anonymous · Answer

thanks