Question

The area of a rectangular serving tray is `3x^2+17x-56`. The width of the tray is `x+8`. What is the length of the tray?

Answer 1

`3x-7`

Explanation:

First and foremost, factorise the area.
Now, in order to factorise that, we must use the cross-multiplication method:
`3x^2+17x-56`

`x \quad \quad \quad \quad` `8`
`3x \quad -7`

On the left-hand side, `x * 3x` makes the first term in the equation which is `3x^2`. On the right-hand side, `8 * (-7)` makes up the last term in the trinomial which is `-56`. Finally, the sum of the cross product `-7*x+8*3x` is equal to the middle term which is `17x`.

Thus

`3x^2+17x-56=(x+8)(3x-7)`

We know that `Area=("length")*("width")`
Therefore, `"length"=(Area)/("width")`
So
`l=(3x^2+17x-56)/(x+8)=((cancel(x+8))(3x-7))/cancel(x+8)=3x-7`