Factoriser (2x+7)(x-1)-4(x-1)

Règle de distributivité de la multiplication par rapport à l'addition

ab + ac = ba + ca = a( b + c)
ou
ab - ac = ba - ca = a( b - c)

Si je remplace (x-1) par a, puis -4 par c, je n'ai plus qu'à remplacer b par (2x+7) pour retrouver la 2e formules qui conduit à factoriser a=(x-1).

ba-ca = a(b-c) c'est (2x+7)(x-1)-4(x-1)
c'est aussi
a(b-c) c'est à dire (x-1)[(2x+7)-4]

= (x-1)(2x+7-4)
= (x-1)(2x+3)

D'où la factorisation recherchée
(2x+7)(x-1)-4(x-1) =(x-1)(2x+3)

Inéquation (x-1)(x+2)<0, x réel

Pour que le produit soit négatif il faut qu'un des 2 facteurs soit négatif et l'autre positif. Il y a 2 combinaisons possibles:

• Produit  -par +
• Produit  + par -

(x-1)(x+2)<0

Si x-1 <0 c'est à dire x< 1, il faut x+2 >0 donc x>-2 donc :
1e solution -2< x < 1

Si x-1 > 0 c'est à dire x > 1 il faut x+2 <0 ce qui est impossible puisque si x > 1 alors x+2 > 3
Il n'y a pas de 2e solution

Se fixer des buts et des priorités

Faisant suite à une première discussion sur "Apprenez-moi comment me planifier" je reprends un schéma développé par le canadien Dave Pollard pour mieux cerner ce qui doit servir de fondement aux buts et priorités qu'on essaye de se fixer au cours de notre existence.

En 2006 (voir liens en bleu ci-dessous), il a proposé ce diagramme de VENN pour relier notre plaisir d'être à nos passions (ce qu'on aime), nos dons (ce qu'on réussi à faire facilement) et notre détermination (à faire ce qui est absolument nécessaire), et ainsi nous aider à fixer nos priorités.

FINDING WHERE YOUR PASSION, YOUR GENIUS, AND YOUR PURPOSE MEET.
Getting Things Done, Happiness, and Our Strange Sense of Priority

Avec ce diagramme, il cerne les 3 critères les plus importants pour se construire une vie agréable et s'efforcer de réunir ses meilleurs atouts, effet  :

• Faire ce qu'on aime vraiment, c'est pouvoir y passer plus de temps que les autres, avec plaisir, et continuer à progresser
• Avoir des aptitudes reconnues et appréciées, c'est le meilleur moyen que les autres vous fassent confiance et fassent appel à vous
• Répondre aux besoins des autres, c'est pouvoir valoriser son travail et satisfaire ses propre besoins, et ainsi éviter de réduire sa vie à une peau de chagrin.

Ce diagramme fournit un cadre de discussion entre parents, éducateurs et élèves, qui devrait leur permettre de mieux s'exprimer, chacun étant

• plus convaincant et mieux assuré, pour expliquer ses choix autour d'un modèle simple
• plus à l'aise quand il s'agit de parler de soi en éliminant tout sentiment de culpabilité de pas savoir répondre

et qui finalement les aide à soutenir une conversation sans s'indigner, fermer le débat ou tuer la conversation, qui à terme devrait aboutir à reconnaître qu'il vaut mieux  

• toujours parlez pour laisser une impression agréable à chacun (pas forcément la même pour tous)

ce qui au final permettra de dissiper tout sentiment de culpabilité lié à la honte de se montrer soi-même, puisqu'on aura l'assurance de donner du plaisir par notre conversation !
 

Remarque : Les amateurs de la planification par GET IT DONE trouveront dans l'article 1 "Finding where ...." comment Dave utilise les numérotations de ses diagrammes pour ventiler ces tâches. Voici le début de cette discussion :

The chart above is a more elaborate version of the Venn diagram I have used in several recent articles. I use this chart when I review the important-but-non-urgent projects on my Getting Things Done list, to decide which of these projects to work on each day. I had originally planned to flag each of these important-but-non-urgent projects with a number from 1 through 7, depending on which area on the chart above it fell into -- and then focus on the projects in area 3 first. But I discovered it isn't as easy as that (it's never that easy, is it?), because of the six questions that I've now added to the chart:

• Does it pay enough? Some of my pet projects don't pay enough to meet my financial needs, so although I love doing them, I'm good at them, and they're needed, I can't do them (at least until my pension kicks in).
• Do you have time for it? Some of my pet projects are enormous, full-time projects, that would require me to stop doing a lot of things that I cannot or don't want to stop doing (yet).
• Is your ability recognized? Some of my pet projects are things that I know I am good at, but lack the formal credentials to have much credibility doing (that applies to a lot of environmental work, and even some professional writing work, that I know I'd do well, but with a background in financial and professional services it's hard to get a hearing when so many biology, environmental science and journalism grads are vying for the same work).
• Is your ability appreciated? Some my pet projects are things that I know I am good at, but others don't particularly appreciate. This is a particular challenge in providing innovation consulting services to clients -- many potential clients really need these services, but want to hire someone who has been doing very similar work for decades (or, they believe that, with minimal facilitation, they can 'do innovation' themselves).
• Is the need recognized? Some of my pet projects are things I know customers need, but (because I'm too far ahead of the curve) they don't yet realize they need (and as we all know, the customer is -- almost -- always right).
• Is the solution affordable? Some of my pet projects are things I know customers need, and they do too, but they can't afford them. Many of these customers are not-for-profit organizations, and they'd love to have me working with them, but I'd have to reduce my rate by 80% to fit within their budget.

So how do I categorize these projects -- career options really -- when because of these 'hitches' they aren't really area 3 projects? And what do I do about the projects that are area 1, 2, 4, or 5 projects -- but might become, or be changed to, area 3 projects with time or dedicated effort?

Let's take the questions one at a time:

• Does it pay enough? If your answer to this is 'no', then I would suggest that 'what's needed' (someone to do this work for little or no remuneration) is not what you have to offer, and this is in fact an area 2 project. You want a six figure income for organic gardening? Area 2.
• Do you have time for it? If you don't, what are you spending your time on? If you, like most of the world, are spending most of your life doing area 5 work (which probably means you're underemployed) maybe it's time to ask yourself whether you should stop and do some area 3 work instead. But ask yourself the six questions first, to make sure your alternative is really area 3 work. If it is, make time for it!
• Is your ability recognized? If your answer to this question is no, then either you need to build the personal credentials so it is (if your job and other time commitments will allow you to), or change jobs for one that does recognize your abilities. In the meantime, you're probably actually doing work you don't love (area 5 work) and which perhaps isn't what you're good at either (area 7 work).
• Is your ability appreciated? This one's easier -- if there's a disconnect between what you're doing and what you know is needed, you're in area 2.
• Is the need recognized? Same answer -- if you're ahead of the market, anticipating its needs before the market is ready for your gift, you're doing area 2 work.
• Is the solution affordable? Same as the 'Does it pay enough?' answer -- area 2.