Answer:
Option D is correct
factored form of the given equation is; (x+2)(x-8)
Explanation:
The given quadratic equation is : \(x^2-6x-16\)
Now, to convert this quadratic equation into factored form;
\(x^2+bx+c =(x+r)(x+s)= x^2+(r+s)x+r\cdot s\)
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;
\(x^2-6x-16\) = \(x^2-8x+2x-16\)
or
\(x^2-8x+2x-16\) = \(x(x-8)+2(x-8)\)
Now taking (x-8) common we get;
\(x(x-8)+2(x-8)\) = \((x+2)(x-8)\)
therefore, the factored form of the \(x^2-6x-16\) is; \((x+2)(x-8)\)
