Show work and Factor 4x^2+xy-18y^2

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

so we want the following to happen:

Notice as well that means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product , then we can consider the case in which one of this  (b or d) is the negative factor. So let's then assume that are positive.

We can then try combinations for    such as:

Just by selecting the first one

we get that

and since

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

Now we have a good combination of parameters to render the factoring form of the original trinomial:

which makes our factorization:

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a