 # (Verifying that degree at most 3 polynomials form a vector space. )...

## Question

(Verifying that degree at most 3 polynomials form a vector space. )
Vector space (V,+,.,R) is a set V for all u, v ∈ V and c, d ∈ R:
Let V = {a3x³ + a2x² +a1x¹ + a0} where a0­3 any real number.
prove the below
1­ u + v ∈ V
2­ u + v = v + u
3­ (u + v) + w = u + (v + w)
4­ (Zero) There is a special vector 0V ∈ V such that u+0V = u for all u in V .
5­ For every u ∈ V there exists w ∈ V such that u + w = 0V .
6­ c ∙ v ∈ V .
7­ (c+d)∙v = c∙v+d∙v.
8­ c∙(u+v) = c∙u+c∙v.
9­ (cd) ∙ v = c ∙ (d ∙ v).
10­ 1∙v =v for all v∈V.

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