SPS SPS FM 2024 October — Question 4

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2024
SessionOctober
TopicFactor & Remainder Theorem
TypeFactorise polynomial completely

4. The polynomial \(P ( x )\) is defined as follows:
\(P ( x ) \equiv x ^ { 8 } + 8 x ^ { 7 } + 28 x ^ { 6 } + 56 x ^ { 5 } + 70 x ^ { 4 } + 56 x ^ { 3 } + 28 x ^ { 2 } + 8 x , x \in \mathbb { R }\)
By first factorising \(P ( x )\) find all of its real roots.
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