// Numbas version: exam_results_page_options {"name": "Polynomials: equating coefficients 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

Suppose that during some working, you find that 

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{poly} $=$ {otherpoly}

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for all $x$.

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Two polynomials are equal if and only if their corresponding coefficients are also equal.

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So we 'equate the coefficients' of the polynomials given in this question, this means that the constant terms must be equal, ie

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\\[\\simplify{{k[0]}=C_0+{j[0]}}\\]

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the coefficients of the $x$ terms must be equal, ie

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\\[\\simplify{{k[1]}={j[1]}C_1+{j[2]}}\\]

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the coefficients of the $x^2$ terms must be equal, ie

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\\[\\simplify{{k[2]}=C_2}\\]

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the coefficients of the $x^3$ terms must be equal, ie

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\\[\\simplify{{k[3]}={j[3]}C_3}\\]

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the coefficients of the $x^4$ terms must be equal, ie

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\\[\\simplify{{k[4]}=C_4/{j[4]}}\\]

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and the coefficients of the $x^5$ terms must be equal, ie

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\\[\\simplify{{k[5]}=C_5/{j[5]}+{j[6]}}.\\]

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Solving equal of these equations for $C_i$ gives our required values.

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Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

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What can be said about the value of $C_i$?

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$C_0=$ [[0]], $C_1=$ [[1]], $C_2=$ [[2]], $C_3=$ [[3]], $C_4=$ [[4]], $C_5=$ [[5]] 

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