Problem

For \(P(x)~=~-2(x~-~1)^4\) plus terms of degree below \(4\), identify the leading parts and leading term, state the degree and leading-coefficient sign, and give \(\text{both}~\text{exact}~\text{end}~\text{limits}\).

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Leading parts: −2 · x⁴ = −2x⁴. Leading term: −2x⁴. Degree/sign: even degree 4, negative leading coefficient. End limits: as x → −∞, P(x) → ∞; as x → ∞, P(x) → ∞.

Leading parts: 2 · x⁴ = 2x⁴. Leading term: 2x⁴. Degree/sign: even degree 4, positive leading coefficient. End limits: as x → −∞, P(x) → ∞; as x → ∞, P(x) → ∞.

Leading parts: −2 · x⁴ = −2x⁴. Leading term: −2x⁴. Degree/sign: even degree 4, negative leading coefficient. End limits: as x → −∞, P(x) → −∞; as x → ∞, P(x) → −∞.

Leading parts: −2 · x⁵ = −2x⁵. Leading term: −2x⁵. Degree/sign: odd degree 5, negative leading coefficient. End limits: as x → −∞, P(x) → ∞; as x → ∞, P(x) → −∞.

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For \(P(x)~=~-2(x~-~1)^4\) plus terms of degree below \(4\), identify the leading parts and leading term, state the degree and leading-coefficient sign, and give \(\text{both}~\text{exact}~\text{end}~\text{limits}\).

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