Factoring Expressions Ex. 4

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Factoring expressions

If the sign of the last term is positive, (1) find two numbers (both will be positive or both will be negative) whose product is the last term and whose sum is the coefficient of the middle term and (2) give both factors the sign of the middle term.įirst check to see whether you can monomial factor (factor out common terms). If the sign of the last term is negative, (1) find two numbers (one will be a positive number and the other a negative number) whose product is the last term and whose difference is the coefficient (number in front) of the middle term and (2) give the larger of these two numbers the sign of the middle term and the opposite sign to the other factor. To decide on the signs of the numbers, do the following. (2) Factor the last term and place the factors in the right sides of the parentheses. Place these factors in the left sides of the parentheses. Then if a = 1 (that is, the first term is simply x 2), use double parentheses and factor the first term. To factor polynomials having three terms of the form ax 2 + bx + c, (1) check to see whether you can monomial factor (factor out common terms). To factor the difference between two squares, (1) find the square root of the first term and the square root of the second term and (2) express your answer as the product of the sum of the quantities from Step 1 times the difference of those quantities.įactoring polynomials having three terms of the form ax 2 + bx + c When the common monomial factor is the last term, 1 is used as a place holder in the second factor.įactoring the difference between two squares To factor out a common factor, (1) find the largest common monomial factor of each term and (2) divide the original polynomial by this factor to obtain the second factor. To factor means to find two or more quantities whose product equals the original quantity. Quiz: Linear Inequalities and Half-Planes.Solving Equations Containing Absolute Value.Inequalities Graphing and Absolute Value.Quiz: Operations with Algebraic Fractions.Solving Systems of Equations (Simultaneous Equations).Quiz: Solving Systems of Equations (Simultaneous Equations).Quiz: Variables and Algebraic Expressions.Signed Numbers (Positive Numbers and Negative Numbers).Quiz: Simplifying Fractions and Complex Fractions.Simplifying Fractions and Complex Fractions.Quiz: Signed Numbers (Positive Numbers and Negative Numbers).Quiz: Multiplying and Dividing Using Zero.Quiz: Properties of Basic Mathematical Operations.Properties of Basic Mathematical Operations.

Commission for @sophia-sol of our understanding and depictions of Oviraptor through time.

I have read Fellowship of the Ring more times than I have cared to keep count and every time I read Boromir’s, well, possession for lack of a better word, I have read it in fear, in discomfort, in horror, indifferently.

This was, I think, the first time I read it in pity. I looked at all the plans Boromir was making, how he would save his beloved city, how obstinate he was in his belief that the men of Minas Tirith would not be corrupted when wielding the Ring against Sauron —and I felt sad. He’s waving his hands and hollering and part of him is desperate just for the Ring, of course he is, he’s been traveling beside it with no hope for months, but he’s also desperate for hope. He’s desperate for a chance to save his people, save his brother, save his city.

Moreover, every time he calls out the Elves or the Wizards, you have to remember that he doesn’t know them. All he knows is that he traveled almost a full year to get their advice and they send him on, in his eyes, a hopeless venture. The one hope they give him is Aragorn, who promises to return and help save Minas Tirith with him, but even that all changes once Gandalf dies. They come to Lothlorien and of course it’s a welcome break, but they cannot, or maybe in Boromir’s eyes will not, help his people. And once they leave, Aragorn assumes his role as leader of the Fellowship in Gandalf’s stead more permanently and suddenly even that one, brief, uncertain hope of his is gone. Aragorn will follow Frodo. And it’s almost certain that Frodo will not go to Minas Tirith.

So is it any wonder, really, that tired, desperate, hopeless Boromir, out of his realm, out of his depth, already hanging by a thread when he joins the Fellowship and having been gnawed on by the Ring for months upon months afterwards, finally snaps once it’s clear that he will have to return home empty-handed and almost certain that somewhere far away Sauron is capturing the Ring and killing the companions that he had bonded with? Of course part of the Ring is making him lust for power, but it’s also his only “reliable” (in his mind) source of hope left to save his city.

And so I read Boromir’s (intelligent and thought out, mind you) raving and I don’t feel scared for Frodo, not after reading it so many times and knowing what ultimately happens, but sorrow for Boromir.

My personal interpretation of Kavetham is that Alhaitham is aware of his feelings for Kaveh and he’s just accepted them, shrugged and continued living his life. It’s just a fact to him now. And if someone asked him if he ever planned on telling Kaveh, he’d be like, “It’s none of his business.”

the newest chapter has me thinking about kdj’s relationship with the fourth wall

Irondad fic ideas #119

We've all seen the fics where the Rogues return and immediately assume that Peter is Tony's son, leading to a "prank" where Tony and Peter "act" like father and son (they soon realize they barely have to act, cue feelings)

Now, a fic that is a twist on that old favorite.

The Rogues return, and they quickly figure out that Peter is not Tony's biological son, that he started as an intern and as Spider-Man but the two have grown closer since then. The Rogues assume that Tony has never told Peter how much he cares about him. They believe Tony is too emotionally constipated, and that Peter must still think he is "just an intern"

However, in assessing the situation, the Rogues have failed to account for some pretty vital facts: 1) the amount of time that has actually passed, and 2) the fact that Tony Stark would do just about anything, even face and overcome his childhood programming, for Peter Parker

Peter and Tony have known each other for two years now. They have already had all the emotional conversations. Peter sees Tony as a father, and Tony sees Peter as a son, and the whole Ironfam knows it. No one is in the dark about what's going on.

...except the Rogues.

When Peter and Tony realize that the Rogues immediately assumed Tony is emotionally incapable, they decide to prank them by seeing just how long they will keep believing that

Around the Rogues, Peter calls Tony "Mr. Stark," and Tony pretends to be a stone cold bitch (even while "subtly" remaining a helicopter parent). Back on their own floor of the tower, Peter switches easily between "Tony" and "Dad," they have movie nights where they fall asleep on the couch together, and dinners with Pepper, May, Rhodey, and Happy.

The Rogues decide they need to help Tony and Peter realize their feelings. This goes on for a long time.

Then, one day, Peter gets hurt. Bad. Maybe he gets hurt as Spider-Man, maybe it's a kidnapping or hostage situation. One way or another, he ends up calling out for his dad.

The Rogues all hold their breath, expecting Tony to be stunned, to freak out and go hide in his lab. But Tony doesn't even blink. He comforts Peter, holds onto him, promises that he's safe

Finally, it becomes clear that the Rogues... might have misjudged the situation. Just a bit.

i think one of the boldest and best moves wolf 359 makes in its character development is that, in terms of the major defining events that led him to where he is, eiffel doesn't have a tragic backstory so much as he is responsible for the tragic backstory of someone else.

(the archetype of the everyman protagonist who copes with past trauma via humor does in many ways describe eiffel, but like with every character in wolf, it's the complexity of their circumstances that make them feel like real people with believable inner worlds. they don't subvert the archetypes they represent, exactly; they're just people, complex and contradictory, who ultimately can't be constrained by the expectations or defined lines of the narratives imposed on them.)

eiffel believes this is an intrinsic part of who he is, that he was "just those mistakes"; he externalizes his desire for redemption and that manifests as lenience towards people who lack his fundamental desire for growth. and in failing to recognize his own ability for growth, he presents himself as a doomed character archetype more than a person; he sidelines himself as an observer within his own story. his guilt and self-hatred allow him to in some way abdicate responsibility, to see his failings as inevitable, and it's only accepting his own complexity and capacity to be more, the human quality he recognizes so fervently in others, that frees him from those self-imposed conceptions.

(once my friend kit said that eiffel “defines the tone and the moral compass of wolf 359 so strongly that if you put him into any other series he would turn it into wolf 359 too” and i think about that a lot.)

doug eiffel is wolf 359, in all it believes, and despite his perception of himself as the weakest link, he is so interwoven with both the crew of the hephaestus and the themes of the show that he is inseparable from either. he doesn't always embody the show's values or its morals - in fact, he frequently fails to live up to them as much as he'd like - but he is the one who advocates for them. "it's not just about surviving; it's about being able to live with ourselves after we get off this tin can."

it's a show about communication; he is an intermediary, a vessel for communication - sometimes literally, and he's also just a guy who is still trying to learn how to communicate better himself. what eiffel represents is a flawed, contradictory, unpredictable, irrepressible humanity, singular, and so desperately in need of connection. the show's love of humanity is truer for that. he has genuinely done wrong, in ways he may not ever be forgiven for. he has very real flaws, some of which persist through the entire show, even as he's consciously trying to do better. and he is very much human, and very much loved.

I'm so grateful that the only GG fans that care about the light novels are the ones that can be normal about things because Lightning the Argent goes from the rawest scenes of carnage imaginable to Ky Kiske doing something mildly religious like offering a short, silent, prayer for someone that got mangled to death by WMD dragons, and I just know that, in the wrong hands, those brief religious moments would generate the most annoying goddamn memes you could ever imagine

"[Elizabeth Woodville's] piety as queen seems to have been broadly conventional for a fifteenth-century royal, encompassing pilgrimages, membership of various fraternities, a particular devotion to her name saint, notable generosity to the Carthusians, and the foundation of a chantry at Westminster after her son was born there. ['On other occasions she supported planned religious foundations in London, […] made generous gifts to Eton College, and petitioned the pope to extend the circumstances in which indulgences could be acquired by observing the feast of the Visitation']. One possible indicator of a more personal, and more sophisticated, thread in her piety is a book of Hours of the Guardian Angel which Sutton and Visser-Fuchs have argued was commissioned for her, very possibly at her request."

-J.L. Laynesmith, "Elizabeth Woodville: The Knight's Widow", "Later Plantagenet and Wars of the Roses Consorts: Power, Influence, Dynasty"

??? is so gorgeous in your art, I'd understand why they would hate MC for not dying in their presence..

thank you (⌒▽⌒) i think they’re more of a “if you die, it’ll be by my hand and my hand only” kind of person! very romantic HAHAHA

I love how your style makes the prototype alternate between creepy and weirdly cute//

Willy would love to eat this salmon... Or catnap, the food down here is already scarce and these anons keep throwing it at others

"If you wish to have it, then you are welcomed to. It's honestly almost insulting how much food keeps getting thrown at me in particular. It's like I'm some stray dog to them. I mean, I am perfectly fine with them giving me food, but why must they throw it and it smack off of my face?"

He says this as he squeezes the anon in his grasp.

rare small post of Few images of witch

Guess who’s been experimenting with a new chibi style

tbh if you think about it we're incredibly lucky that muse's been around for like 30 years and still go on tours / haven't disbanded / noone's dead yet

Bad time of it, all things considered (Patreon)