Question

What is the factored form of x2 – 6x – 16? (x – 4)(x – 2) (x 4)(x – 2) (x – 2)(x 8) (x – 8)(x 2)

Answer 1

Hello,

x²-6x-16=x²+2x-8x-16=x(x+2)-8(x+2)=(x+2)(x-8)

Answer D.

Answer 2

Option D is correct

factored form of the given equation is; (x+2)(x-8)

Step-by-step 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)`