Question

Write an expression in factored form for the area of the shaded portion of the figure. (In the figure, a = 3 and b = 5.)

The figure is in this website below:
www.webassign.net/laratrmrp6/p-3-162-alt.gif

The answer i got: (5(x+5)^2)/6 - 15/2. but online website (where i do my assignments that is posted by my teacher), says it is wrong, i just don't understand why.

Answer 1

Your answer is mathematically correct, but it's in vertex form.
Expand and simplify it to put it in factored form.

Answer 2

Area of big triangle A1 = 1 / 2 [ 5 / a ∙ ( x + b ) ]

Area of small triangle A2 = 1 / 2 ( 5 ∙ a )

Area of shaded portion = Area of big triangle - Area of small triangle

A = A1 - A2

A = 1 / 2 ( 5 / a ) ∙ ( x + b ) ( x + b ) - 1 / 2 ( 5 ∙ a ) =

1 / 2 [ 5 / a ∙ ( x + b )² - 5 a ] =

1 / 2 [ 5 / a ∙ ( x + b )² - 5 a² / a ] =

1 / 2a [ 5 ∙ ( x + b )² - 5 a² ] =

5 / 2a [ ( x + b )² - a² ) ] =

5 / 2a ( x + b + a ) ( x + b - a )

_____________________________
Remark:

m² - n² = ( m + n ) ( m - n)

so

( x + b )² - a² = ( x + b + a ) ( x + b - a )
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Answer 3

Thanks Bosnian