Four is a zero of the equation x3+3x2−18x−40=0. Which factored form is equivalent to the equation? (x+4)(x+2)(x+5)=0
(x−4)(x+2)(x+5)=0
(x−4)(x+4)(x+5)=0
(x+2)(x−4√)(x+4√)=0
Answers
One zero of the equation is given and that is 4.
It is not present in the 1st factored form (x+4)(x+2)(x+5)=0.
So we consider the 2nd Factored form and that is
(x−4)(x+2)(x+5)=0
x - 4 = 0 , x + 2 = 0 , x + 5 = 0
x = 4 ( already given, x = -2 , x = - 5
So we shall check x = - 2 and x = -5 by putting in x^3+3 x^2−18 x−40=0 one by one.
Putting x = - 2 , we get
(-2)^3 +3 (-2)^2 - 18(-2) - 40 = 0
- 8 + 3(4) + 36 - 40 = 0
- 8 + 12 + 36 - 40 = 0
0 = 0 Satisfied
So x = -2 is a zero of given equation.
Putting x = - 5 , we get
(-5)^3 +3 (-5)^2 - 18(-5) - 40 = 0
- 125 + 3(25) + 90 - 40 = 0
- 125 + 75 + 90 - 40 = 0
0 = 0 Satisfied
So x = - 5 is also a zero of given equation.
So (x−4)(x+2)(x+5)=0 is factored form of the given equation.