Canonical URI: https://w3id.org/kmath/textbook_solution/donga_solution_p145_p033_14
| rdf:type | math:TextbookSolution |
|---|---|
| rdfs:label | 동아 p033 단원 마무리 14 풀이 |
| rdfs:comment | 동아 공통수학1 정답 및 풀이 p145-p146의 p033 단원 마무리 14 풀이. |
| math:answerText | \(P(x)=(x+1)^3+2(x+1)^2+2(x+1)+1,\quad 1020201\) |
| math:explanationText | \[ P(x)=x^3+5x^2+9x+6 \] \[ =(x+1)(x^2+4x+5)+1 \] \[ =(x+1)\{(x+1)(x+3)+2\}+1 \] \[ =(x+1)[(x+1)\{(x+1)+2\}+2]+1 \] \[ =(x+1)^3+2(x+1)^2+2(x+1)+1 \] 양변에 \(x=99\)를 대입하면 \[ P(99)=100^3+2\times100^2+2\times100+1=1020201 \] 이다. |
| math:mappingConfidence | 1.0 |
| math:pageEnd | 146 |
| math:pageStart | 145 |
| math:problem | textbook_problem:donga_vision_p033_14 |
| math:reviewStatus | reviewed |
| math:solutionKind | worked_solution |
| math:usesSolutionPattern | solution_pattern:coefficient_comparison_identity |
| math:usesSolutionPattern | solution_pattern:polynomial_division_algorithm |