Question

PICK A B C D What are the factors of the quadratic

Answer 1

The point of this exercise is to find the factorization of the polynomial on the left:

`x^2{\textcolor{red}{+}}8x\textcolor{green}{-}65`

Its factorization has the form:

`(x{{\textcolor{red}{+}}a_1)}(x{\textcolor{green}{-}a_2}_{})`

where the first sign (red +) coincides with the first + above, and the second sign (green -) coincides with the product between the signs above (red + by the green - ). Now, we must find the missing (two) numbers a_1 and a_2. These numbers must satisfy:

`\begin{cases}a_1-a_2=8 \\ a_1\cdot a_2=-65\end{cases}`

Solving this system "by eye", we get

`a_1=13,a_2=5`

Then, the factorization is

`(x+13)(x-5)`

The answer would be C if there were a 13 instead of 12.