Question

Four is a zero of the equation x3+3x2−18x−40=0. Which factored form is equivalent to the equation? (x−4)(x+4)(x+5)=0 (x+4)(x+2)(x+5)=0 (x+2)(x−4√)(x+4√)=0 (x−4)(x+2)(x+5)=0

Answer 1

Answer : (x-4)(x+2)(x+5) =0

Four is a zero of the equation $x^3+3x^2 - 18x - 40=0$

4 is one of the zero of the given equation.

Lets use synthetic division method to divide by the zero 4

We write all the coefficients of each term

 4            1           3          -18         -40

               0          4           28          40

            ----------------------------------------------------

               1           7            10            0

Now frame an equation from the answer we got

$1x^2 + 7x + 10 =0$

Now we factor the left hand side

(x+2) (x+5) =0

4 is one of the zero so factor is (x-4)

The factors of equation is $x^3+3x^2 - 18x - 40=0$

(x-4)(x+2)(x+5) =0