cormac's copy of Divide Polynomials

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cormac breen 6 years, 6 months ago

Created this as a copy of Divide Polynomials.

Name	Status	Author	Last Modified
Divide Polynomials	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Divide Polynomials: Cubic by linear	draft	Ben Brawn	11/09/2017 04:05
cormac's copy of Divide Polynomials	draft	cormac breen	30/10/2018 15:53
Luis's copy of Divide Polynomials	draft	Luis Hernandez	30/11/2018 01:09
Luis's copy of Divide Polynomials	draft	Luis Hernandez	30/11/2018 14:55
Dividir un polinomio cúbico $p(x)=ax^3+bx^2+cx+d$ por $q(x)=mx+n$ , para hallar el cociente y el resto.	Ready to use	Luis Hernandez	19/06/2023 13:34
Divide Polynomials	draft	Xiaodan Leng	10/07/2019 23:21

There are 11 other versions that do you not have access to.

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	6
s2	integer	1
s1	integer	1
m	integer	1
al	integer	-8
n	integer	-6
s	integer	7
r	integer	1
t	integer	6

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-9..9)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

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

Parts

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

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$q(x)=\;\;$ 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

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

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

MATH1901 CA V2 by cormac breen in cormac's workspace.
MATH1901 Quadratic Equations & Further Algebra by Blathnaid Sheridan in Blathnaid's workspace.
MATH1901 CA by cormac breen in cormac's workspace.
Laura MATH1901 by Blathnaid Sheridan in Blathnaid's workspace.
MATH1901 (Laura's Group) by Laura Cooke in Laura's workspace.
MATH1901 (Paul&Laura) by Blathnaid Sheridan in Blathnaid's workspace.
MATH1901 Continuous Assessment by Paul Molloy in Paul's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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cormac breen 6 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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cormac's copy of Divide Polynomials

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

cormac breen 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`