How to factorize polynomialsHow to factorize $x^3 - 7x + 6$?How to factorize an equation?Factorize the...
Is this answer explanation correct?
Why didn't Boeing produce its own regional jet?
Unlock My Phone! February 2018
Is this draw by repetition?
How can I deal with my CEO asking me to hire someone with a higher salary than me, a co-founder?
Does the Idaho Potato Commission associate potato skins with healthy eating?
What Exploit Are These User Agents Trying to Use?
What is the opposite of "eschatology"?
Why do I get negative height?
Avoiding the "not like other girls" trope?
How does a dynamic QR code work?
How to find if SQL server backup is encrypted with TDE without restoring the backup
Why is it a bad idea to hire a hitman to eliminate most corrupt politicians?
Processor speed limited at 0.4 Ghz
In Bayesian inference, why are some terms dropped from the posterior predictive?
Car headlights in a world without electricity
Venezuelan girlfriend wants to travel the USA to be with me. What is the process?
How dangerous is XSS
Is there a hemisphere-neutral way of specifying a season?
Placement of More Information/Help Icon button for Radio Buttons
Notepad++ delete until colon for every line with replace all
Is it possible to create a QR code using text?
What do you call someone who asks many questions?
Why was Sir Cadogan fired?
How to factorize polynomials
How to factorize $x^3 - 7x + 6$?How to factorize an equation?Factorize the polynomial $x^3+y^3+z^3-3xyz$Factorize PolynomialsFactorize polynomial in $mathbb Z_2[X]$Factorize x^3+3Factorize $x^4+n(2-n)x^2+n^2$ into irreducible polynomials over Q for any natural number n.Factorize into irreducible polynomialsFactorize a third degree polynomialCan we factorize a second order matrix polonymial?
$begingroup$
How can I factorize the polynomial $$-a(b-c)(x-b)(x-c)-b(c-a)(x-a)(x-c)-c(a-b)(x-a)(x-b)?$$ Please show me the whole process step by step in an easy way.
polynomials
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
asked Sep 4 '15 at 14:54
RaisaRaisa
334
$endgroup$
add a comment |
$begingroup$
How can I factorize the polynomial $$-a(b-c)(x-b)(x-c)-b(c-a)(x-a)(x-c)-c(a-b)(x-a)(x-b)?$$ Please show me the whole process step by step in an easy way.
polynomials
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
asked Sep 4 '15 at 14:54
RaisaRaisa
334
$endgroup$
add a comment |
$begingroup$
How can I factorize the polynomial $$-a(b-c)(x-b)(x-c)-b(c-a)(x-a)(x-c)-c(a-b)(x-a)(x-b)?$$ Please show me the whole process step by step in an easy way.
polynomials
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
asked Sep 4 '15 at 14:54
RaisaRaisa
334
$endgroup$
How can I factorize the polynomial $$-a(b-c)(x-b)(x-c)-b(c-a)(x-a)(x-c)-c(a-b)(x-a)(x-b)?$$ Please show me the whole process step by step in an easy way.
polynomials
polynomials
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
asked Sep 4 '15 at 14:54
RaisaRaisa
334
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
asked Sep 4 '15 at 14:54
RaisaRaisa
334
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
edited Sep 4 '15 at 14:56
Ángel Mario Gallegos
18.5k11330
18.5k11330
asked Sep 4 '15 at 14:54
RaisaRaisa
334
asked Sep 4 '15 at 14:54
RaisaRaisa
334
asked Sep 4 '15 at 14:54
RaisaRaisa
334
334
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
It is a quadratic polynomial, whose coefficient of $x^2$ is given by:
$$ -sum_{cyc}a(b-c) = sum_{cyc}ac-sum_{cyc}ab = 0. $$
Its value at $x=0$ is also zero since $sum_{cyc}(b-c)=0$, too.
It follows that your polynomial is some multiple of $x$.
Which multiple? That is easy to understand, by evaluating at $x=a$, for instance.
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
$endgroup$
$begingroup$
$(a - b) (b - c) (c-a) x$
$endgroup$
– Iuʇǝƃɹɐʇoɹ
Sep 4 '15 at 15:01
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1422013%2fhow-to-factorize-polynomials%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
It is a quadratic polynomial, whose coefficient of $x^2$ is given by:
$$ -sum_{cyc}a(b-c) = sum_{cyc}ac-sum_{cyc}ab = 0. $$
Its value at $x=0$ is also zero since $sum_{cyc}(b-c)=0$, too.
It follows that your polynomial is some multiple of $x$.
Which multiple? That is easy to understand, by evaluating at $x=a$, for instance.
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
$endgroup$
$begingroup$
$(a - b) (b - c) (c-a) x$
$endgroup$
– Iuʇǝƃɹɐʇoɹ
Sep 4 '15 at 15:01
add a comment |
$begingroup$
It is a quadratic polynomial, whose coefficient of $x^2$ is given by:
$$ -sum_{cyc}a(b-c) = sum_{cyc}ac-sum_{cyc}ab = 0. $$
Its value at $x=0$ is also zero since $sum_{cyc}(b-c)=0$, too.
It follows that your polynomial is some multiple of $x$.
Which multiple? That is easy to understand, by evaluating at $x=a$, for instance.
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
$endgroup$
$begingroup$
$(a - b) (b - c) (c-a) x$
$endgroup$
– Iuʇǝƃɹɐʇoɹ
Sep 4 '15 at 15:01
add a comment |
$begingroup$
It is a quadratic polynomial, whose coefficient of $x^2$ is given by:
$$ -sum_{cyc}a(b-c) = sum_{cyc}ac-sum_{cyc}ab = 0. $$
Its value at $x=0$ is also zero since $sum_{cyc}(b-c)=0$, too.
It follows that your polynomial is some multiple of $x$.
Which multiple? That is easy to understand, by evaluating at $x=a$, for instance.
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
$endgroup$
It is a quadratic polynomial, whose coefficient of $x^2$ is given by:
$$ -sum_{cyc}a(b-c) = sum_{cyc}ac-sum_{cyc}ab = 0. $$
Its value at $x=0$ is also zero since $sum_{cyc}(b-c)=0$, too.
It follows that your polynomial is some multiple of $x$.
Which multiple? That is easy to understand, by evaluating at $x=a$, for instance.
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
edited Sep 4 '15 at 15:01
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
answered Sep 4 '15 at 15:00
Jack D'AurizioJack D'Aurizio
292k33284672
292k33284672
$begingroup$
$(a - b) (b - c) (c-a) x$
$endgroup$
– Iuʇǝƃɹɐʇoɹ
Sep 4 '15 at 15:01
add a comment |
$begingroup$
$(a - b) (b - c) (c-a) x$
$endgroup$
– Iuʇǝƃɹɐʇoɹ
Sep 4 '15 at 15:01
$begingroup$
$(a - b) (b - c) (c-a) x$
$endgroup$
– Iuʇǝƃɹɐʇoɹ
Sep 4 '15 at 15:01
$begingroup$
$(a - b) (b - c) (c-a) x$
$endgroup$
– Iuʇǝƃɹɐʇoɹ
Sep 4 '15 at 15:01
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1422013%2fhow-to-factorize-polynomials%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
