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If (x + 8) is a factor of f(x), which of the following must be true?

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If (x + 8) is a factor of f(x), which of the following must be true?

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AP Calculus AB Multiple Choice 1998 Exam Part B (solutions...)

AP Calculus AB Multiple Choice 1998 Exam Part B (solutions…) – Which of the following statements about f is false? 77. Let f be the function given by f(x) = 3e2x and let g be the function given by g(x) = 6×3. At what value of x do the graphs of f and g have parallel tangent lines? 78. The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second.B.)Neither x = -8 nor x = 8 is a root of f(x). Find the width of the rectangle.? 8 answers.Out of the given options. option C f(-8) = 0 is correct.

If (x + 8) is a factor of f(x), which of the following must be true? – What must be a factor of $f(x)$? The question is from a SAT practice test. I'm not entirely sure what the question is asking. At first I thought that the $x Then I thought, that the $x$ table values must be multiplied by the equations to get $f(x)$, for example, in the equation $x-3$ multiplied by $0$ if $x$ is…Start by trying this out with a few odd functions that you know of, functions like f(x) = x. You'll quickly eliminate one of the choices this way. As for the other two, it's tough to find any odd function to show that they're false, so it might be that they are true. How can you be sure though?Answer to Which of the following statements are true?(a) An object can move even when no force acts on it.(b) If an object isn't m… Question: Which Of The Following Statements Are True?(a) An Object Can Move Even When No Force Acts On It.(b) If An Object Isn't Moving, No External Forces…

If (x + 8) is a factor of f(x), which of the following must be true?

If (x + 8) is a factor of f(x), which of the following must be true? – Scoring well on GMAT Reading Comprehension is a critical factor for nailing a perfect score. If x is positive, y must be positive Again, by the same example as above (when x = 2), we see that St. II is not always true either. Since we know by now that St. I and II are not MUST BE TRUE statements, we…The question asks us which answer choices must be an even integer , so it likely tests our Integers math skill. We want to know which answer choice MUST be even. Looking at the answer choices, we have addition, multiplication, and subtraction all throughout.Add Your Explanation. You must have a Magoosh account in order to leave an explanation. Improve Your Score. Magoosh SAT is an affordable online course for studying the SAT. Learn More About Magoosh.

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How To Solve The 6s Challenge – 嗨,你所觀看的是Presh Talwalkar 的MindYourDecisions 這裡有一個非常有趣的數字難題 你從複製三個相同的數字開始,
而且每個數字都必須等於6 而謎題就是要讓每個方程都為正確,
並且使用常用的數學運算 你必須遵守兩個規則 第一,你能不加入新的數值 舉個例子吧,像是不能用立方根的運算,
因為它包含了數值3 第二個規則是,你必須使結果等於6。
你不能使用不等於6的數 我要先感謝 Tyler Cenko 建議我這個數學謎題,然後我也感謝
來自巴西的 Caio Cerqueira 也向我建議這個題目 而我也想介紹我的解法,
我的影片將會讓你知道如何聰明的解開一切難題,
像是我們將討論的這個題目將會變得很簡單 在這個影片中你將會看見許多人們 詢問一些難題,然而這就是最好證明
這個頻道正在教全世界的朋友們如何解數學 所以,你弄清楚了ㄇ 試著解解看這個難題,當你準備好之後,
就看一看我是如何解題的吧 所以,我該如何解題呢 我將會提出一些多樣的解答 基於時間的限制,我只能介紹幾些解法,而剩下的
就該靠你自己喽 創造一些方程式去解題目吧 讓所有人在討論中知道你的答案吧 我會先解決直接抑或是簡單的問題 讓我們從2 2 2等於6開始 我們可以通過使用等式2加2加2等於6來解決這個問題 所以我們已經弄清楚了一題 現在6 6 6也很相似,我們可以取6加6減去6得出6 或者我們也可以做6乘以6除以6等於6 對於我們集合的解決方案。讓我們來看第一個方程式 現在讓我們解決7 7 7等於6。我們可以做到這一點,因為7減去7除以7等於6 對於5 5 5我們也得到了非常相似的解決方案,我們可以取5加5除以5等於6 目前為止,一切都挺順利的。 現在,讓我們解決3 3 3等於6的方程式 一種解決方法是3乘3減3等於6 但是實際上還有更多解決方法 另一個是3階乘加3減3等於6 我們也可以做3階乘乘以3除以3等於6 或者我們可以做一些事情,例如平方根 平方根3乘以3,然後我們可以加3,也等於6 因此,出於演示目的,我將取3乘以3減去3等於6 現在讓我們解決9 9 9等於6 我們可以使用的一個技巧是讓這9個數字都取平方根 這是一個簡單的數學家小撇步 由於9的平方根等於3,我們將問題簡化為3 3 3等於6 這個問題以前已經解決了 因此,我們對3 3 3等於6的任何解決方案也將適用 將此9 9 9應用於每個9的平方根 所以我們可以將其求解為9的平方根乘以9的平方根減9的平方根等於6 也可以將9的平方根階乘的平方根 再加上9的平方根減去9的平方根等於6
不然,其實也有一些其他的解 9的平方根階乘乘以9除以9等於6 讓我們把這整個算式等於六。 出於演示目的。我只考慮第一個方程式 現在讓我們回到4等於4等於4的情況再一次我們可以取這些數字的平方根 同樣,我們有一個簡單的把戲,因為四的平方根等於2我們將問題簡化為2 2 2等於6 之前已曾解決了。 例如,我們取這些數字的總和會等於6 但是,如果您不想這樣做,也可以將數字用4減去4除以4 我們把那個算式乘以階乘 我們也可以使用4的平方根加4除以4 我們用這個算式乘以階乘,也等於6 所以出於演示目的,我們只考慮第一個方程 現在讓我們解決10 10 10等於6 讓我們逐步推演 我們將10減去10除以10,我們的結果將等於9 好吧,現在取這個算式的平方根會得到結果3 然後我們將算式乘以階乘 這樣我們就能得到10 10 10-等於6 那現在,1 1 1呢? 請注意,如果我們將3個數字相加就會得出3,然後將算式乘以階乘得到6 那我們如何求解0 0 0等於6?首先,我們將採用這些數字乘以階乘 我們再次使用數學家的把戲 由於0階乘等於1,我們已將問題簡化為1 1 1等於6,之前已解決。 因此,我們將這些數字相加,然後取總和的階乘,即等於6 最後我們如何求解8 8 8等於6?許多人認為這是所有這些方程式中最困難的 所以我們將按部就班地來對付他 我們取8加8等於16 我們將平方根放上16的平方根,取其平方根,並且16的平方根等於4 然後,我們取那個的平方根的平方根 因此16的平方根的平方根等於2 現在我們將8減去2就會等於6 所以這是解決這個問題的一種方法 但是,解決此問題的另一種方法是,您可以將8加8除以8,等於9 然後我們取9的平方根,等於3,然後取3的階乘 那會等於6 就是這樣了。我們以弄清楚瞭如何在每個等式中得到6 你知道了嗎? 謝謝收看這些數學視頻 那些被激發並建立信心的全世界的人們,我們已經擁有超過一億的觀看次數 雖然無情的數學從未給予他們回饋 讓我們更加積極地去破解數學吧。請免費訂閱以獲取最新視頻,以提供幫助 觀看和分享所有mind your decisions的視頻和視頻 您可以通過presh [at] mindyourdecisions [dot] com向我發送拼圖或數學主題的電子郵件 如果您想這麼做 您可以查看視頻說明中列出的我的書。您可以在Patreon上支持我,以獲得獨家獎勵 感謝收看,感謝您的支持 .

❖ Synthetic Division – A Shortcut for Long Division! ❖ – In this video we're gonna do an example of what's called synthetic division Synthetic division is when you're basically dividing a polynomial by a first degree polynomial so x to the first power it may or may not have a number in there if it was just x you would just break things up individually that'd be easy anyway So suppose we wanna divide, again, x cubed minus 2x squared plus 3x minus 4 we're gonna divide that by (x-2) What you do in this case is this Whatever we're dividing by…
So notice there's a minus 2 — it's x minus 2 we actually take the opposite sign and use positive 2 and that's what you stick outside And then notice I have 1 x cubed minus 2x squared plus 3x minus 4 Notice there's no terms missing. It starts from the third degree second degree first degree and then we just have a number All we do is write the coefficients So there's a 1 a negative 2 in front of the x squared so a positive 3 in front of the x and there's a negative 4 just hanging out And with synthetic division what you do is the first term you just drop it right down there's nothing to do And then the idea is we multiply So I'm gonna take positive 2 times 1, and then stick that number in the next spot So it says postive 2 times 1 will give us positive 2 And then what we do is we add those numbers together in this column So negative 2 plus 2 is gonna give me zero And then we repeat this process Now we take positive 2, multiply by zero and then we stick it in the next column So it says positive 2 times zero is just gonna give us zero So if we add those together we get positive 3 And then again I take positive 2 times positive 3 I'm just gonna erase my little red dots here Take positive 2 times positive 3, that'll give me positive 6 We add the column together and we get the number 2 This last number is gonna be your remainder If I could spell correctly here And what it says is, in summary, it says We can actually — So the numbers in the bottom are what are important 'Kay so it says we can actually rewrite x cubed minus 2x squared plus 3x minus 4 divided by (x-2) So I'll just keep my numbers at the bottom It says we can actually write that as — Okay so the highest power is x cubed and to make things one degree less so this is gonna go with my x squared term this is gonna go with my x term this is gonna be my constant and again the other part is my remainder It says we can actually write x cubed minus 2x squared plus 3x minus 4 divided by (x-2) as 1 x squared plus zero x So usually zero x we'll leave out so I'll erase it So 1 x squared plus 3 and then my remainder is 2 and we put that over what we were originally dividing by which is (x-2) And now we have broken up our original fraction into something a little bit more simple So this would be your solution after you did the synthetic division So a useful little trick One other thing I wanna point out about synthetic division Notice that if we look at the thing on top If I call that f(x) So if I say f(x) equals x cubed minus 2x squared plus 3x minus 4 Suppose I wanted to evaluate this — Suppose I want to plug in the number 2 Well it turns out if you plug in the number 2 If you do the synthetic division with (x-2), if you do that synthetic division it says whatever the remainder is that is actually gonna be the solution when you plug that value in So just a coincidence here that I plug 2 in and got 2 out But notice if I plug 2 in I'll get 2 cubed minus 2 times 2 squared plus 3 times 2 minus 4 So this is 8 minus 8 plus 6 minus 4 Well the 8 and the 8 cancel out positive 6 minus 4 is, hey, positive 2 Okay, so synthetic division is actually also a way to evaluate polynomials That remainder, again, is gonna be your solution And sometimes if you have a real tedious problem, using synthetic division can be useful For example if you're plugging things into a calculator Typically I don't use it, really hardly ever but that's just a personal preference of mine so Alright, I hope this example makes some sense I think I'm gonna do one other as well and just kinda reinforce this stuff If you have any questions just send me an email .