Coefficients and Polynomial

Question

What are the coefficients and constant of the polynomial 5x^3+3+2x^5−x when rewritten in descending order, using a coefficient or constant of 0 for any missing terms? Enter your answer as a list of integers separated by commas. For example, if the polynomial is 42x^4−53x^3+64x^2+75, enter your answer like this: 42, -53, 64, 0, 75.

Answer 1

Recall that a polynomial can be rewritten as a_n xⁿ + a_n-1 x^n-1 +... + a₁ x¹ + a₀ x⁰ , n being the highest degree.

Rewrite 5x³ +3 + 2x⁵ −x as 2x^{5 +} 5x³ - x + 3 and notice that the highest degree is 5 and we are missing some terms. You may rewrite these missing terms with 0 coefficients and rewrite as:

2x⁵ + 0x⁴ + 5x³ + 0x² -1x +3. Now you can write coefficients as 2, 0, 5, 0, -1, 3

Answer 2

That would be rewritten as 2x⁵ + 0x⁴ + 5x³ + 0x² -1x +3 so the coefficients and constant are 2, 0, 5, 0, -1, 3