Create a polynomial that describes the perimeter of the outside figure: x + 8, 5, x, x, 2x, x + 8, 34 and inside figure: x + 12.
Because the x^2 is 2x^2 you cannot find factors of 28 that add to 15
Jessica is correct, it is factorable
2x^2 + 8x + 7x + 28
(2x + 7)(x + 4)
To create a polynomial that describes the perimeter of the outside figure, let's start by listing all the sides:
Outside Figure:
- Side 1: x + 8
- Side 2: 5
- Side 3: x
- Side 4: x
- Side 5: 2x
- Side 6: x + 8
- Side 7: 34
Inside Figure:
- Side 1: x + 12
The perimeter of a figure is the sum of all its sides. So, to find the polynomial, we need to add up all the sides of the outside figure.
Perimeter of the Outside Figure = Side 1 + Side 2 + Side 3 + Side 4 + Side 5 + Side 6 + Side 7
= (x + 8) + 5 + x + x + 2x + (x + 8) + 34
To simplify this expression, we first combine like terms. We add all the x terms together and all the constant terms (numbers without variables):
= x + x + x + x + 2x + 8 + 8 + 5 + 34
= 6x + 55
Therefore, the polynomial that describes the perimeter of the outside figure is 6x + 55.