# Thread: using a polynomial equation

1. ## using a polynomial equation

Any help will be greatly appreciated

An envelope is 4cm longer then it is wide. The area is 96 sq. cm Find the length and width. Use a polynomial equation.

2. $\displaystyle \begin{gathered} S_{envelope} = w(w + 4) = 96 \hfill \\ w^2 + 4w - 96 = 0 \hfill \\ \end{gathered}$

solve the quadratic equation to obtain the solution

3. am i doing this correctly?
w-12=0
+12 +12
w=12

w+8=0
-8 -8
w=-8

am i doing this correctly?
w-12=0
+12 +12
w=12

w+8=0
-8 -8
w=-8
Plug your numbers in back into the original equation for Area and see. Hint: Remember that width, length, cannot be negative.

5. would it be
12(12+4)=96

6. 12*(12+4)= 12*16 =192 so that's cant be right.

the factoring of your polynomial should be (x-8)(x+12) which gives you x-8 = 0 or x+12 = 0, meaning x=8 or x=-12. Since x is a length and cant be negative the answer must be x=8.

Does it work?

8*(4+8) = 8*12 = 96!

7. so what i was doing before
w-12=0
+12 +12
w=12

w+8=0
-8 -8
w=-8
was going in the total wronge direction?

8. No, it is just that your signs were backwards.

(w-8)(w+12) = w^2 + 4w - 96

where as

(w+8)(w-12) = w^2 - 4w - 96

Notice that the first quadratic equation is the one you are working with. The second equation above is similar to the first but the middle w-term is negative when it should be positive.