Question

The area of a rectangular field is given by the triomial t²-4t-45. THe length of the rectangle is t+5. What is the expression for the width of the field?

Answer 1

The area of a rectangle is A = l*w
If we do a bit of trivial algebra, we can rearrange that to be \[w = \frac{A}{l}\]

We know \(A = t^2-4t-45\)
and \(l = t+5\)

So if we plug in our values for \(A\) and \(l\) we get
\[w = \frac{t^2-4t-45}{t+5}\]

At this point, either factor the numerator and hope something cancels out, or do the polynomial division by long division or synthetic division.

Answer 2

@JaneDoe100

Factor t^2 - 4t - 45 and post what you get here. Okay?

Answer 3

I dont think that can be factored since there are no like terms

Answer 4

What are two numbers that multiply to a*c = 1*(-45) = -45 AND add to b= -4 ?

The expression t^2 - 4t - 45 will factor.

Answer 5

@JaneDoe100 What about those numbers?

Answer 6

-45 -5 -4 -1 1 4 5 45

Answer 7

these are the factors but in there pairs none of them add to -4

Answer 8

How about -9 and +5 ?

Answer 9

t^2 - 4t - 45 = t^2 - 9t + 5t -45 =

t(t - 9) + 5 (t - 9) =

(t - 9) (t + 5)

Answer 10

Area of Rectangle = Length times Width
t²-4t-45 = (t + 5) W

(t - 9) (t + 5) = (t + 5) W

[(t - 9) (t + 5)] / (t +5) = W

(t - 9) = W --> @JaneDoe100

Answer 11

To do this by straight division:

t -9
-------------------
t+5 | t^2 - 4t -45
- ( t^2 +5t ) <- "t" is biggest value we can multiply with (t+5)
---------
-9t - 45
- (-9t - 45) <- 9 is biggest value we can multiply with (t+5)
------------
0

W = t-9