Answer:
Option D is correct
factored form of the given equation is; (x+2)(x-8)
Explanation:
The given quadratic equation is : [tex]x^2-6x-16[/tex]
Now, to convert this quadratic equation into factored form;
[tex]x^2+bx+c =(x+r)(x+s)= x^2+(r+s)x+r\cdot s[/tex]
So, r and s must satisfy:
r+s=b
rs =c
Now, we are looking for a pair of numbers whose product is -16 such as (4,−4), (1, -16), (2, -8). They also have to add up to -6.
The only choice that satisfies both is (2 , -8).
then;
[tex]x^2-6x-16[/tex] = [tex]x^2-8x+2x-16[/tex]
or
[tex]x^2-8x+2x-16[/tex] = [tex]x(x-8)+2(x-8)[/tex]
Now taking (x-8) common we get;
[tex]x(x-8)+2(x-8)[/tex] = [tex](x+2)(x-8)[/tex]
therefore, the factored form of the [tex]x^2-6x-16[/tex] is; [tex](x+2)(x-8)[/tex]
