Question

Please me with this, thank you to whoever helps.

Answer 1

Answer: b= x²-8

Explanation:

Given:

A= 1/2 b h

A= 1/2 ( x³ + 8x² -8x -64)

h= x+8

Solution:

A= 1/2 b h >substitute what you know

1/2 ( x³ + 8x² -8x -64) = 1/2 b (x+8) >simplify

b=
`(x^(3) + 8x^(2) -8x -64)/(x+8)`

There are 2 ways to solve this. You can solve by factoring the polynomial or dividing.

Solution by Division:

Synthetic Division is easiest:

-8 | 1 8 -8 -64

| -8 0 64

1 0 -8 0 => x²-8 = b

OR

Solution by Factoring:

b=
`(x^(3) + 8x^(2) -8x -64)/(x+8)` > group first 2 terms on top and 2nd 2 terms on top

b=
`((x^(3) + 8x^(2) )( -8x -64))/(x+8)` >take out gcf of both groupings

b=
`(x^(2) (x + 8 )-8( x +8))/(x+8)` > take out x+8 on top as gcf

b=
`( (x + 8 )( x^(2) -8))/(x+8)` > cancel x+8 from top and bottom

b= x²-8