Four is a zero of the equation x^3+3x^2−18x−40=0.
Which factored form is equivalent to the equation?
A. (x+2)(x−√4)(x+√4)=0
B. (x−4)(x+2)(x+5)=0
C. (x+4)(x+2)(x+5)=0
D. (x−4)(x+4)(x+5)=0
if four is a zero then (x-4) is a factor
so we divide x3+3x2−18x−40 by (x−4)to determine what the other factors might be.x3+3x2−18x−40x−4=x2+7x+10
This quotient is easy enough to factor as x2+7x+10=(x+5)(x+2)and thusx3+3x2−18x−40=(x−4)(x+2)(x+5)this is choice B
