Challenging +1.2 This question requires recognizing binomial coefficients (Pascal's triangle row 8) to factor as x(x+1)^8, then finding the straightforward roots x=0 and x=-1. While pattern recognition is needed, the coefficients are given explicitly making this easier than deriving them, and the factorization leads directly to the answer without complex algebraic manipulation.
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. [0pt]
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.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2024 Q4 [6]}}