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Long Division of Polynomials

Divide ${{r m} x^{3} + {n r + m s} x^{2} + {n s + t r} x + {t n + be}}$ by ${{r} x + {s}}$ so that:

\frac{{{r m} x^{3} + {n r + m s} x^{2} + {n s + t r} x + {t n + be}}}{{{r} x + {s}}} = q (x) + \frac{r}{{{r} x + {s}}}

where $q (x)$ is the quotient polynomial and $r$ is the remainder ( $r$ is a constant).

The coefficients of $q (x)$ are integers, do not input as decimals.

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", "name": "Ann'srough 9Oct18 copy of Ann's copy of Long division, single digit divisor results in no remainder", "functions": {}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "parts": [{"extendBaseMarkingAlgorithm": true, "scripts": {}, "customMarkingAlgorithm": "", "sortAnswers": false, "showCorrectAnswer": true, "unitTests": [], "marks": 0, "showFeedbackIcon": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "

Divide the polynomial $\\simplify{{a}{c}x^2+({a}{d}+{b}{c})x+{b}{d}}$ by the linear function $\\simplify{{a}x+{b}}$

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The simplest case. Divisor is single digit. There is no remainder.

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reconsider.. randomise a and b such that a.b=n0 and a+b=n1

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this will be the quotient 'answer' i.e. (x+b) for quadratic numerator

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