The area of a rectangle is 2x^2+5x^2-x-6 cm. write a polynomial that represents its width if its length is 2x^2+ x-3.
You must have meant:
area is 2x^3+5x^2-x-6
if so, then it factors nicely into
(x-1)(x+2)(2x+3)
and the width of 2x^2 + x - 3 factors to (2x+3)(x-1)
then
(2x^3+5x^2-x-6) รท (2x^2+ x-3)
= (x-1)(x+2)(2x+3)/( (2x+3)(x-1) )
= x+2
or
you could do a long algebraic division as it stands and also get x+2
thanks a lot!
Math
To find the width of the rectangle, we need to divide the area by the length.
Step 1: Write the area polynomial as A(x) = 2x^2 + 5x^2 - x - 6 cm.
Step 2: Write the length polynomial as L(x) = 2x^2 + x - 3 cm.
Step 3: Divide the area polynomial by the length polynomial:
- w(x) = A(x) / L(x)
- w(x) = (2x^2 + 5x^2 - x - 6) / (2x^2 + x - 3)
Since w(x) is the width polynomial, the answer is w(x) = (2x^2 + 5x^2 - x - 6) / (2x^2 + x - 3) cm.