Add: $2 x^{3} - 9 x^{2} + 8, 3 x^{2} - 6 x - 5, 7 x^{3} - 10 x + 1$ and $3 + 2 x - 5 x^{2} - 4 x^{3}$ .

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Solution

Let us add the given expressions $2 x^{3} - 9 x^{2} + 8, 3 x^{2} - 6 x - 5, 7 x^{3} - 10 x + 1$ and $3 + 2 x - 5 x^{2} - 4 x^{3}$ as shown below:

$(2 x^{3} - 9 x^{2} + 8) + (3 x^{2} - 6 x - 5) + (7 x^{3} - 10 x + 1) + (3 + 2 x - 5 x^{2} - 4 x^{3}) = 2 x^{3} - 9 x^{2} + 8 + 3 x^{2} - 6 x - 5 + 7 x^{3} - 10 x + 1 + 3 + 2 x - 5 x^{2} - 4 x^{3} = (2 x^{3} + 7 x^{3} - 4 x^{3}) + (- 9 x^{2} + 3 x^{2} - 5 x^{2}) + (- 6 x - 10 x + 2 x) + (8 - 5 + 1 + 3) (C o m b i n i n g l i k e t e r m s) = (2 + 7 - 4) x^{3} + (- 9 + 3 - 5) x^{2} + (- 6 - 10 + 2) x + 7 = 5 x^{3} - 11 x^{2} - 14 x + 7$

Hence, $(2 x^{3} - 9 x^{2} + 8) + (3 x^{2} - 6 x - 5) + (7 x^{3} - 10 x + 1) + (3 + 2 x - 5 x^{2} - 4 x^{3}) = 5 x^{3} - 11 x^{2} - 14 x + 7$ .

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