1. Which expression belongs in the space?
|---------------
x-2 |x^2 + 7x - 18
-(x^2-2x)
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18
a.5x - 18
b.5x + 18
c.9x - 18
d. 9x + 18
To find the expression that belongs in the space, we need to subtract one polynomial from another. Let's break down the steps:
1. Start by distributing the negative sign to each term in the second polynomial. When we distribute a negative sign, it changes the sign of each term. So, -(x^2 - 2x) becomes -x^2 + 2x.
2. Now, subtract the two polynomials by subtracting their corresponding terms.
x^2 + 7x - 18
- (-x^2 + 2x)
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x^2 + 7x - 18 + x^2 - 2x
3. Combine like terms. In this step, we can add or subtract terms with the same variables and exponents.
x^2 + 7x + x^2 - 2x - 18
4. Simplify the expression. Combine the x^2 terms, the x terms, and the constant term to get the final expression.
2x^2 + 5x - 18
Therefore, the correct expression that belongs in the space is 2x^2 + 5x - 18.
None of the provided answer choices (a. 5x - 18, b. 5x + 18, c. 9x - 18, d. 9x + 18) matches this expression.