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Edufirst
Answer: option D. 2x^2 + (3/2)x  - 5

Explanation:

1) polynomials given:

 f(x) = x/2 - 2 and g(x) = 2x^2 + x - 3

2) question: find (f + g) (x)

That means that f(x) + g(x), so you have to add up the two polynomials given.

3) x/2  - 2 + 2x^2 + x - 3

4) Combine like terms:

a) terms with x^2: you only have 2x^2, so it is not combined with other term.

b) terms with x: x/2 + x

that is a sum of fractions: x/2 + x = [x + 2x] / 2 = 3x / 2 = (3/2)x

c) constant terms: - 2 + (-3) = - 2 - 3 = - 5

5) Result: 2x^2 + (3/2)x - 5

That is the option d.


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