Factor Theorem

Error

There was an error loading the page.

Contributors

Mark Hodds

History

○

Mark Hodds 7 years ago

Created this as a copy of Marlon's copy of Finding the missing value of a constant in a polynomial, using the Factor Theorem .

Name	Status	Author	Last Modified
Finding the missing value of a constant in a polynomial, using the Factor Theorem	Ready to use	Elliott Fletcher	20/11/2019 14:39
Factor Theorem and polynomials	draft	Adrian Jannetta	16/08/2023 14:56
Finding the missing value of a constant in a polynomial, using the Factor Theorem	draft	Adrian Jannetta	16/08/2023 14:56
Marlon's copy of Finding the missing value of a constant in a polynomial, using the Factor Theorem	draft	Marlon Arcila	03/02/2018 16:11
Marlon's copy of Finding the missing value of a constant in a polynomial, using the Factor Theorem	draft	Marlon Arcila	03/02/2018 16:19
Factor Theorem	draft	Mark Hodds	24/03/2018 15:58
Dado que $({x+{d}})$ es un factor de $g(x) = ax^3+{b}x^2+{x}+m$ , Encontrar el valor de $m$ .	Ready to use	Luis Hernandez	19/06/2023 13:36
JD's copy of Finding the missing value of a constant in a polynomial, using the Factor Theorem	draft	JD Ichwan	21/05/2019 05:42
Finding the missing value of a constant in a polynomial, using the Factor Theorem	draft	Xiaodan Leng	11/07/2019 01:38

There are 4 other versions that do you not have access to.

Question statement

The factor theorem states that if $f(x)$ is a polynomial and $f(p) = 0$ , then $(x-p)$ is a factor of $f(x)$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

w	integer	4
a	integer	3
b	integer	1
d	integer	2
coef_x3	number	-32
coef_x2	number	60
coef_x	integer	-34

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2,3,4)

JME function reference

Description

Random number between 2,3,4.

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:

coef_x
coef_x2
coef_x3

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

Given that $(\simplify{x+{d}})$ is a factor of $g(x) = \simplify{{w}*x^3+({w}{d}+{a}+{w}{b})*x^2+({a}{d}+{w}{b}{d}+{a}{b})*x}+m$ , find the value of $m$ .

$m =$ Unnamed gap.

Advice

Using the factor theorem, we know that if $(x-a)$ is a factor of a polynomial $f(x)$ , then $f(a)=0$ .

We are given that $(\simplify{x+{d}})$ is a factor of $g(x) = \simplify{{w}*x^3+({w}{d}+{a}+{w}{b})*x^2+({a}{d}+{w}{b}{d}+{a}{b})*x+m}$ .

By the factor theorem, this means that $g(\simplify{-{d}}) = 0$ .

Substituting $x=\simplify{-{d}}$ into $g(x)$ gives

$\begin{align} g(\simplify{-{d}}) &= \simplify[all,!collectNumbers]{{coef_x3}+{coef_x2}+{coef_x}+m}\\ &=\simplify{{coef_x3}+{coef_x2}+{coef_x}+m}. \end{align}$

Therefore, as $g(\simplify{-{d}}) = 0$ , we have

$\begin{align} \simplify{{coef_x3}+{coef_x2}+{coef_x}+m}&=0\\ m&=\simplify{-({coef_x3}+{coef_x2}+{coef_x})}. \end{align}$

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

This question is used in the following exams:

Factor Theorem by Mark Hodds in Tutoring.
exam1 by haifa abd in haifa's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Mark Hodds 7 years ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Factor Theorem

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Mark Hodds 7 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`