Question

WILL GIVE YOU FAN AND MEDAL!!!!!!

Part A: The area of a square is (9x2 - 12x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (3 points)

Part B: The area of a rectangle is (25x2 - 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (2 points)

Part C: The volume of a rectangular box is (x3 - 7x2 - 9x + 63) cubic units. Determine the dimensions of the rectangular box by factoring the volume expression completely. Show your work. (5 points)

Answer 1

@iGreen

Answer 2

Do you know what the formula for the area of a square is?

Answer 3

The formula is:

\(A = s^2\)

Plug in the area:

\((9x^2 - 12x + 4) = s^2\)

To solve you have to square both sides:

\(\sqrt{(9x^2 - 12x + 4)} = s\)

Which simplifies to: \(\sqrt{(2-3x)^2}\)

Answer 4

so sorry was afk

Answer 5

No problem..I think that solves Part A for you..

Answer 6

so all that is A right?

Answer 7

ok, ty on to B i see it and understand

Answer 8

The formula for the area of a rectangles is \(A = lw\)

Area = \((25x^2 - 16y^2)\)

If we factor this into two separate expressions, they will be the length and the width.

If you factor this you get \((5x - 4y)(5x+4y)\), which represents the dimensions of the rectangle.

Answer 9

and this is all of B right?

Answer 10

Yep.

Answer 11

awesome on to C :)

Answer 12

\( (x^3 - 7x^2 - 9x + 63)\)

For part C, we have to factor this too, but into three parts instead of two, because the area of a rectangular prism is \(A = lwh\).

We get \((x-7)(x-3)(x+3)\) when we factor, so those will be the dimensions of the rectangular box.

Answer 13

That takes care of C..