Dividing Polynomials

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Bill Foster

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Bill Foster 55 years, 3 months ago

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Question statement

Divide $\displaystyle{\simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}}$ by $\simplify[std]{{r}x+{s}}$ so that:

$\frac{\simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}}{\simplify[std]{{r}x+{s}}}=q(x)+\frac{r}{\simplify[std]{{r}x+{s}}}$

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.

Give any introductory information the student needs.

			Name	Type	Generated Value

be	integer	5
s2	integer	-1
s1	integer	1
m	integer	1
al	integer	9
n	integer	3
s	integer	2
r	integer	1
t	integer	1

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random(-9..9)

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Generated value: `integer`

→ Used by:

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"Unnamed part" → "Gap 1." - Minimum accepted value
"Unnamed part" → "Gap 1." - Maximum accepted value

Parts

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1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Number entry
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Gap-fill

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$q(x)=\;\;$ Gap 0.

Input all numbers as integers and not as decimals.

$r=\;\;$ Gap 1.

Advice

We have:

$\begin{eqnarray*} \simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}&=&\simplify[std]{(x+{s})x^2+{n}x^2+{n*s+t}x+{t*n+be}}\\&=&\simplify[std]{(x+{s})x^2+(x+{s})*{n}x+{t}x+{t*n+be}}\\ &=&\simplify[std]{(x+{s})x^2+(x+{s})*{n}x+(x+{s})*{t}+{t*n+be-s*t}}\\ &=&\simplify[std]{(x+{s})(x^2+{n}x+{t})+{t*n+be-s*t}} \end{eqnarray*}$

Hence

$\frac{\simplify[std]{{r * m} * x ^ 3 + {n * r + m * s} * x ^ 2 + {n * s + t * r} * x + {t * n + be}}}{\simplify[std]{{r}x+{s}}}=\simplify[std]{x^2+{n}x+{t}+{t*n+be-s*t}/({r}x+{s})}$

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This question is used in the following exams:

mathcentre: Polynomial division by Bill Foster in Bill's workspace.
Dividing polynomials 1 by Bill Foster in Bill's workspace.
Bradford: Dividing polynomials 1 by Bill Foster in Bill's workspace.
Maths Support: Polynomial division by Christian Lawson-Perfect in Maths Support Wiki.
Bradford: Diagnostic test - Basic maths by Bill Foster in Bill's workspace.
Basic Maths Revision by Gareth Woods in Gareth's workspace.
mathcentre: Diagnostic test - Basic maths by Bill Foster in Bill's workspace.
maths skills 1 by cormac murphy in cormac's workspace.
Harry's copy of Maths Support: Polynomial division by Harry Flynn in Harry's workspace.

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Taxonomy: mathcentre

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Bill Foster 55 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Dividing Polynomials

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`