Divide Polynomials

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Bill Foster

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Bill Foster 6 years, 6 months ago

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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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

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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	-9
s2	integer	-1
s1	integer	-1
m	integer	1
al	integer	-3
n	integer	8
s	integer	-9
r	integer	1
t	integer	5

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.

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Generated value: `integer`

-9

This variable doesn't seem to be used anywhere.

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

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

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Part	Test	Passed?
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Mathematical expression
Mathematical expression		Hasn't run yet
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Bill Foster 6 years, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Divide Polynomials

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`