Pythagoras0: /* 메타데이터 */ 새 문단

2022-08-12T03:20:46Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2022-08-12T03:20:44Z

노트: 새 문단

새 문서

== 노트 ==

===말뭉치===
# Synthetic division carries this simplification even a few more steps.<ref name="ref_266e57c2">[https://courses.lumenlearning.com/waymakercollegealgebra/chapter/synthetic-division/ Synthetic Division]</ref>
# In synthetic division, only the coefficients are used in the division process.<ref name="ref_266e57c2" />
# How To: Given two polynomials, use synthetic division to divide Write k for the divisor.<ref name="ref_266e57c2" />
# Show Solution Begin by setting up the synthetic division.<ref name="ref_266e57c2" />
# Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor — and it only works in this case.<ref name="ref_3b5fbb06">[https://www.purplemath.com/modules/synthdiv.htm How does synthetic division of polynomials work?]</ref>
# Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.<ref name="ref_3b5fbb06" />
# In the synthetic division, I divided by x = −3, and arrived at the same result of x + 2 with a remainder of zero.<ref name="ref_3b5fbb06" />
# The advantages of synthetic division are that it allows one to calculate without writing variables, it uses few calculations, and it takes significantly less space on paper than long division.<ref name="ref_2293905d">[https://en.wikipedia.org/wiki/Synthetic_division Synthetic division]</ref>
# The above form of synthetic division is useful in the context of the polynomial remainder theorem for evaluating univariate polynomials.<ref name="ref_2293905d" />
# Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm.<ref name="ref_60c0891a">[https://mathworld.wolfram.com/SyntheticDivision.html Synthetic Division -- from Wolfram MathWorld]</ref>
# For an example of synthetic division, consider dividing by .<ref name="ref_60c0891a" />
# (x - 3) , let's compare long division to synthetic division to see where the values are the same.<ref name="ref_59892b1a">[https://mathbitsnotebook.com/Algebra2/Polynomials/POPolySynDivide.html Polynomial Synthetic Division]</ref>
# As was done with long division, synthetic division must also fill in missing terms in the dividend.<ref name="ref_59892b1a" />
# Let's see what happens if we use our regular synthetic division process, and ignore the fact that the leading coefficient of the divisor is 2 (not 1).<ref name="ref_59892b1a" />
# Now, we have an equivalent problem where the denominator resembles what we have seen previously in our synthetic division questions (a leading coefficient of one).<ref name="ref_59892b1a" />
# We use synthetic division to evaluate polynomials by the remainder theorem, wherein we evaluate the value of \(p(x)\) at \(a\) while dividing \((\frac{p(x)}{(x – a)})\).<ref name="ref_cfda77d0">[https://www.effortlessmath.com/math-topics/how-to-divide-polynomials-using-synthetic-division/ How to Divide Polynomials Using Synthetic Division?]</ref>
# Among these two methods, the shortcut method to divide polynomials is the synthetic division method.<ref name="ref_3fc2c60d">[https://byjus.com/maths/synthetic-division/ Synthetic Division (Definition, Steps and Examples)]</ref>
# In the synthetic division method, we will perform multiplication and addition, in the place of division and subtraction, which is used in the long division method.<ref name="ref_3fc2c60d" />
# The process of the synthetic division will get messed up if the divisor of the leading coefficient is other than one.<ref name="ref_3fc2c60d" />
# Frequently Asked Questions on Synthetic Division What is meant by synthetic division?<ref name="ref_3fc2c60d" />
# Synthetic division is a simplified method of dividing a polynomial by another polynomial of the first degree.<ref name="ref_4579b638">[https://study.com/academy/lesson/synthetic-division-definition-steps-examples.html Steps & Examples - Video & Lesson Transcript]</ref>
# However, synthetic division uses only the coefficients and requires much less writing.<ref name="ref_abf34f25">[https://www.openalgebra.com/2013/10/synthetic-division.html OpenAlgebra.com: Synthetic Division]</ref>
# To understand synthetic division, we walk you through the process below.<ref name="ref_abf34f25" />
# In this case, we use 0 as placeholders when performing synthetic division.<ref name="ref_abf34f25" />
# In this case, a shortcut method called synthetic division can be used to simplify the rational expression.<ref name="ref_c7751c39">[https://sciencing.com/difference-division-synthetic-division-polynomials-8619791.html The Difference Between Long Division & Synthetic Division of Polynomials]</ref>
# It is a Super Fun way to engage students in practice and review of synthetic division and the remainder theorem.<ref name="ref_49b3660b">[https://www.teacherspayteachers.com/Browse/Search:synthetic%20division Synthetic Division Teaching Resources]</ref>
# Solution: This one is a little tricky, because we can only do synthetic division with a linear binomial with no leading coefficient, and this divisor has a leading coefficient of 2.<ref name="ref_4afd1efe">[https://www.theproblemsite.com/reference/mathematics/algebra/polynomials/synthetic-division Synthetic Division: Polynomials]</ref>
# So we can't use synthetic division.<ref name="ref_4afd1efe" />
# However, we can use synthetic division using the binomial (x - 1/2).<ref name="ref_4afd1efe" />
# It turns out that we often use synthetic division when trying to find roots, and if (2x - 1) is a factor, then so is (x - 1/2), so it works out well to do this.<ref name="ref_4afd1efe" />
# Luckily there is something out there called synthetic division that works wonderfully for these kinds of problems.<ref name="ref_3ad1f6b9">[https://tutorial.math.lamar.edu/classes/alg/dividingpolynomials.aspx Dividing Polynomials]</ref>
# In order to use synthetic division we must be dividing a polynomial by a linear term in the form \(x - r\).<ref name="ref_3ad1f6b9" />
# Example 2 Use synthetic division to divide \(5{x^3} - {x^2} + 6\) by \(x - 4\).<ref name="ref_3ad1f6b9" />
# Show Solution Okay with synthetic division we pretty much ignore all the \(x\)’s and just work with the numbers in the polynomials.<ref name="ref_3ad1f6b9" />
# Synthetic division is a shortcut way of dividing polynomials.<ref name="ref_08848c19">[https://www.omnicalculator.com/math/synthetic-division Synthetic Division Calculator With Steps]</ref>
# Synthetic division is most commonly used when dividing by linear monic polynomials x - b .<ref name="ref_08848c19" />
# Keep in mind that synthetic division works for any polynomial divisors: for non-monic polynomials as well as for polynomials of degrees higher than one.<ref name="ref_08848c19" />
# So, let's dive in and learn how to divide polynomials using synthetic division!<ref name="ref_08848c19" />
# Here is how to do this problem by synthetic division.<ref name="ref_3bce67cd">[https://www.themathpage.com/aPreCalc/synthetic-division.htm Topics in precalculus]</ref>
# We will use synthetic division to divide f(x) by x + 4.<ref name="ref_3bce67cd" />
# Use synthetic division to divide f(x) by x − 7.<ref name="ref_3bce67cd" />
# Use synthetic division to divide g(x) by x + 2.<ref name="ref_3bce67cd" />
# Synthetic division can make life easier when you are dividing polynomials.<ref name="ref_fe7c7d6f">[https://jdmeducational.com/synthetic-division-with-coefficient-not-1-or-a-quadratic-divisor/ Synthetic Division With Coefficient Not 1 (Or A Quadratic Divisor) – JDM Educational]</ref>
# So, can you use synthetic division with a coefficient that is not 1?<ref name="ref_fe7c7d6f" />
# You need a monic linear divisor to use synthetic division.<ref name="ref_fe7c7d6f" />
# You can also divide by a quadratic divisor by using synthetic division repeatedly.<ref name="ref_fe7c7d6f" />
# One way is to use synthetic division.<ref name="ref_1c5a40d0">[https://www.dummies.com/article/academics-the-arts/math/pre-calculus/how-to-guess-and-check-real-roots-3-testing-roots-by-dividing-polynomials-using-synthetic-division-167858/ How to Guess and Check Real Roots — 3 — Testing Roots by Dividing Polynomials Using Synthetic Division]</ref>
# You could’ve used synthetic division to do this, because you still get a remainder of 100.<ref name="ref_1c5a40d0" />
# Throw them out with synthetic division!<ref name="ref_9896f513">[https://virtualnerd.com/texas-digits/txh-alg-2/polynomials/dividing-polynomials/What-is-Synthetic-Division What is Synthetic Division?]</ref>
# Then we are ready to use synthetic division.<ref name="ref_56685b8a">[http://mathcentral.uregina.ca/QQ/database/QQ.09.06/h/edward1.html Synthetic division]</ref>
===소스===
<references />

← 이전 판		2022년 8월 12일 (금) 03:20 판
54번째 줄:		54번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q7662748 Q7662748]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'synthetic'}, {'LEMMA': 'division'}]

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Pythagoras0: /* 메타데이터 */ 새 문단

Pythagoras0: /* 노트 */ 새 문단