# 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?

May 27, 2017

$3 x - 7$

#### Explanation:

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

$x \setminus \quad \setminus \quad \setminus \quad \setminus \quad$ $8$
$3 x \setminus \quad - 7$

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

Thus

$3 {x}^{2} + 17 x - 56 = \left(x + 8\right) \left(3 x - 7\right)$

We know that $A r e a = \left(\text{length")*("width}\right)$
Therefore, "length"=(Area)/("width")
So
$l = \frac{3 {x}^{2} + 17 x - 56}{x + 8} = \frac{\left(\cancel{x + 8}\right) \left(3 x - 7\right)}{\cancel{x + 8}} = 3 x - 7$