Which of the following is a polynomial with roots 2, –2, and 2 ?

a.x3 – 4x2 + 4x – 16
b.x3 + 4x2 + 4x + 16
c. x3 + 2x2 + 4x + 8
d.x3 – 2x2 + 4x – 8

Question

Which of the following is a polynomial with roots 2, –2, and 2 ? 

a.x3 – 4x2 + 4x – 16 
b.x3 + 4x2 + 4x + 16 
c. x3 + 2x2 + 4x + 8 
d.x3 – 2x2 + 4x – 8

anonymous · Answer

since the roots are 2, 2, and -2, the choice will be the one that matches $\large (x-2)^2(x+2) $ when expanded (multiplied out....)

asnaseer · Answer

an alternative approach is to use the fact that if $r_1$ is a root of some polynomial function $f(x)$, then:$$f(r_1)=0$$

anonymous · Answer

even better ^^^ :)

asnaseer · Answer

@dpaInc your approach is also valid. and in cases where the polynomial is very long, it might be easier to expand using your version that to calculate a value using my approach.
@RachRach basically use whichever approach you find easiest.

anonymous · Answer

OKay thanks (:

asnaseer · Answer

yw :)

phi · Answer

for (x-2)(x+2)(x-2)
notice that the last (constant term) will be -2*2*-2= +8    
if you are lucky, only one of the choices has a +8, and that would be the answer.