Dado que $({x+{d}})$ es un factor de $g(x) = ax^3+{b}x^2+{x}+m$, Encontrar el valor de $m$.

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Luis Hernandez

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6 years, 3 months ago

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Luis Hernandez 6 years, 3 months ago

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Luis Hernandez 6 years, 3 months ago

Created this as a 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

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Question statement

El teorema del factor establece que si $f (x)$ es un polinomio y $f (p) = 0$ , entonces $(x-p)$ es un factor de $f (x)$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

w	integer	3
a	integer	-1
b	integer	2
d	integer	1
coef_x3	number	-3
coef_x2	number	8
coef_x	integer	-3

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

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1. Gap Mathematical expression
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Dado que $(\simplify{x+{d}})$ es un factor de $g(x) = \simplify{{w}*x^3+({w}{d}+{a}+{w}{b})*x^2+({a}{d}+{w}{b}{d}+{a}{b})*x}+m$ , Encontrar el valor de $m$ .

$m =$ Unnamed gap.

Advice

Usando el teorema del factor, sabemos que si $(x-a)$ es un factor de un polinomio $f(x)$ , entonces $f(a)=0$ .

Se nos da que $(\simplify{x+{d}})$ es a factor of $g(x) = \simplify{{w}*x^3+({w}{d}+{a}+{w}{b})*x^2+({a}{d}+{w}{b}{d}+{a}{b})*x+m}$ .

Por el teorema del factor, esto significa que $g(\simplify{-{d}}) = 0$ .

Sustituyendo

$x=\simplify{-{d}}$ sobre

$g(x)$ obtenemos

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

Por lo tanto, como $g(\simplify{-{d}}) = 0$ , tenemos

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

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Dado que $({x+{d}})$ es un factor de $g(x) = ax^3+{b}x^2+{x}+m$ , Encontrar el valor de $m$ .

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Luis Hernandez 6 years, 3 months ago

Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Dado que (x+d)({x+{d}}) es un factor de g(x)=ax3+bx2+x+mg(x) = ax^3+{b}x^2+{x}+m, Encontrar el valor de mm.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Luis Hernandez 6 years, 3 months ago

Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Dado que $({x+{d}})$ es un factor de $g(x) = ax^3+{b}x^2+{x}+m$ , Encontrar el valor de $m$ .

Generated value: `integer`