Bob Morgan
04/22/2024 · Primary School
Find the remainder when \( 8 x^{3}+4 x^{2}+6 x+7 \) is divided by \( 2 x+1 \) Given the sets \( T=\{a, c, d, e\} \) and \( S=\{b, c, d, f\} \), find \( T \cap S \quad\{c, d\} \). Prove that the sum of the series \( 1^{2}+2^{2}+3^{2}+\ldots+n^{2} \) is \( \frac{n}{6}(n+1)(2 n+1) \)
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1. The remainder of \( 8x^{3}+4x^{2}+6x+7 \) divided by \( 2x+1 \) is found using polynomial long division.
2. The intersection of sets \( T \) and \( S \) is \( \{c, d\} \).
3. The sum of the series \( 1^{2}+2^{2}+3^{2}+\ldots+n^{2} \) is \( \frac{n}{6}(n+1)(2n+1) \), proven by mathematical induction.
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