Two is a zero of the equation x^3−x^2−14x+24=0.Which factored form is equivalent to the equation?A) (x+4)(x−2√)(x+2√)=0B) (x−2)(x+2)(x+4)=0C) (x−3)(x−2)(x+4)=0D) (x−3)(x+2)(x+4)=0 THE ANSWER IS C ) (x-3)(x-2)(x+4)=0trust me on this.
Accepted Solution
A:
Answer: The factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4). Step-by-step explanation:Since 2 is a zero of the equation [tex]x^{3} - x^{2} -14x + 24 = 0[/tex]Therefore, (x - 2) is a factor of the equation [tex]x^{3} - x^{2} -14x + 24 = 0[/tex]Now, on dividing [tex]x^{3} - x^{2} -14x + 24 = 0[/tex] by (x - 2) we get, [tex](x - 2) (x^{2} + x - 12)[/tex] as shown in Fig(1)On factorising x² + x - 12= x² + x - 12= x² + 4x - 3x - 12= x (x + 4) - 3 (x + 4)= (x - 3) (x + 4)Now, [tex](x - 2) (x^{2} + x - 12)[/tex] = [tex](x - 2) (x -3) (x + 4)[/tex] So the factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4). Therefore option (c) is the correct answer.