QuestionSheila is ordering stickers for the front of her. interactive notebook. Sheila's math teacher is only allowing students to decorate in the green area of their interactive notebook. Sheila doesn't want to buy more stickers than she needs. The area for the space that must stay bare is represented by 9 stickers only allow book She $\left(2 x^{2}-x+3\right)$ . The entire area of the front of her notebook is represented by Por thes pe entire a farts the $\left(x^{2}+5 x-4\right)$ .What is the area of allowed space for decorations? Answer Area for stickers a

Studdy Solution

STEP 1

1. The area of the entire front of the notebook is given by the polynomial $x^2 + 5x - 4$ .
2. The area that must stay bare is given by the polynomial $2x^2 - x + 3$ .
3. The area for stickers is the difference between the total area and the bare area.

STEP 2

1. Set up the expression for the area of allowed space.
2. Subtract the bare area from the total area.
3. Simplify the resulting expression.

STEP 3

To find the area of the allowed space for decorations, we need to subtract the bare area from the total area.

STEP 4

Write the expression for the area of allowed space as: $(x^2 + 5x - 4) - (2x^2 - x + 3)$

STEP 5

Distribute the negative sign through the second polynomial: $x^2 + 5x - 4 - 2x^2 + x - 3$
Combine like terms: - Combine the $x^2$ terms: $x^2 - 2x^2 = -x^2$ - Combine the $x$ terms: $5x + x = 6x$ - Combine the constant terms: $-4 - 3 = -7$
The simplified expression for the area of allowed space is: $-x^2 + 6x - 7$
The area of allowed space for decorations is:
$\boxed{-x^2 + 6x - 7}$

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