March 26
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This document provides steps and examples for factoring trinomials of the form ax^2 + bx + c. It begins with reviewing special cases like difference of squares and perfect square trinomials. It then outlines a 6-step process for factoring general trinomials: 1) multiply the leading coefficient and constant, 2) find factors of their product that sum to the middle term, 3) rewrite replacing the middle term, 4) factor by grouping, 5) factor out common binomials, 6) check for complete factorization. Examples are provided applying these steps to fully factor trinomials.
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March 25, 2014
The document provides an agenda and notes for a math class focusing on factoring polynomials. Tomorrow's lesson will cover factoring trinomials and the difference of squares, while today covers perfect square trinomials, a warm-up on factoring practice, and a review of techniques for factoring completely. It also lists Khan Academy topics and an upcoming factoring test on specific methods.
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The document discusses three special factoring formulas:
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The document discusses factoring perfect square trinomials. It defines a perfect square trinomial as having the first and last terms as perfect squares, and the middle term twice the product of the first and last terms. The document provides examples of factoring perfect square trinomials using the multiplication breaker map (MBM) method. This involves taking the square root of the first and last terms, checking if the middle term satisfies the definition, and then factoring the expression as the sum or difference of the two terms squared. The document concludes with an activity having students work in groups to factor various perfect square trinomials using MBM.
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The document provides an agenda and notes for a math class focusing on factoring polynomials. Tomorrow's lesson will cover factoring trinomials and the difference of squares, while today covers perfect square trinomials, a warm-up on factoring practice, and a review of techniques for factoring completely. It also lists Khan Academy topics and an upcoming factoring test on specific methods.
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The document discusses three special factoring formulas:
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3) The sum or difference of two cubes can be factored into a binomial times a trinomial using specific formulas.
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This document provides instructions for factoring binomial and trinomial expressions. It explains that factoring trinomials involves first finding the greatest common factor (GCF), and if the expression has a power of x greater than two after factoring the GCF, to move to another step. It also discusses using the quadratic formula to factor trinomials if none of the factor combinations are correct. The goal is to help the reader learn how to factor binomials and trinomials.
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Matlab lecture 8 – newton's forward and backword interpolation@taj copyTajim Md. Niamat Ullah Akhund
Matlab lecture 8 – newton's forward and backword interpolation@taj copy
.
This lecture is from my class lectures in IIT-JU.
.
Find me:
Website: https://www.tajimiitju.blogspot.com
Linked in: https://www.linkedin.com/in/tajimiitju
Researchgate: https://www.researchgate.net/profile/Tajim_Md_Niamat_Ullah_Akhund
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Facebook: https://www.facebook.com/tajim.mohammad
Gitlab: https://gitlab.com/users/tajimiitju
Google+: plus.google.com/+tajimiitju
Email: tajim.mohammad.3@gmail.com
Twitter: https://twitter.com/Tajim53Factoring the difference of two squares
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Matlab lecture 8 – newton's forward and backword interpolation@taj copyTajim Md. Niamat Ullah Akhund
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.
This lecture is from my class lectures in IIT-JU.
.
Find me:
Website: https://www.tajimiitju.blogspot.com
Linked in: https://www.linkedin.com/in/tajimiitju
Researchgate: https://www.researchgate.net/profile/Tajim_Md_Niamat_Ullah_Akhund
Youtube: https://www.youtube.com/tajimiitju?sub_confirmation=1
Slideshare: https://www.slideshare.net/TajimMdNiamatUllahAk
Facebook: https://www.facebook.com/tajim.mohammad
Gitlab: https://gitlab.com/users/tajimiitju
Google+: plus.google.com/+tajimiitju
Email: tajim.mohammad.3@gmail.com
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The document provides notes and examples on factoring trinomials of the form (ax^2 + bx + c) where a is greater than 1. It discusses three methods: grouping, using a box method, and trial and error. Students are reminded to complete their Khan Academy assignments by that night and that there will be new topics on Monday. They are also instructed to do the class work and study guide questions to prepare for their test.
Factoring Polynomials (1).pptx
The document discusses factoring polynomials and finding the roots of polynomial equations. It defines polynomials and polynomial equations. It then covers several methods for factoring polynomials, including factoring polynomials with a common monomial factor, factoring polynomials that are a difference of squares, factoring trinomials, and factoring polynomials by grouping. It also discusses using the factors to find the solutions or roots of a polynomial equation, which are also known as the zeros of a polynomial function.
March 27, 2015
This document provides notes and examples on solving quadratic equations. It begins with an agenda for the day which includes warm up exercises, class notes on solving quadratics, and a factoring test. The class notes section defines quadratic equations, explains their standard form and graph as a parabola, and provides examples of solving various quadratics by factoring. It also discusses properties of parabolas such as having two solutions. The document concludes by providing examples and steps for solving different types of quadratics by factoring and taking square roots.
1.5 Quadratic Equations.pdf
This document provides instruction on factoring polynomials and quadratic equations. It begins by reviewing factoring techniques like finding the greatest common factor and factoring trinomials and binomials. Examples are provided to demonstrate the factoring methods. The document then discusses solving quadratic equations by factoring, putting the equation in standard form, and setting each factor equal to zero. An example problem demonstrates solving a quadratic equation through factoring. The document concludes by assigning homework and an optional reading for the next class.
Factoring
The document discusses various factoring techniques, including:
- Factoring by greatest common factor (GCF)
- Factoring trinomials of the form ax^2 + bx + c by finding two numbers that multiply to c and add to b
- Factoring the difference of two squares and perfect square trinomials
- Using the "box method" to factor trinomials by placing factors of the first and last terms in the boxes
- Factoring by grouping polynomials with four terms into two groups of two terms each.
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Factoring Polynomials with Common Monomial Factor.pptx
Factoring Polynomials with Common Monomial Factor.pptx
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March 26
- 1. 1 Today: Factoring (ax2 + bx + c) Trinomials Review of all other factoring methods/test review Class Work
- 3. 3 Review: Perfect Square Trinomial (x² + 8x + 16) Remember, a PST factors into either a square of a sum or a square of a difference. Use the FOIL method to factor the following: (x² + 4x + 4x + 16) = (x + 4)² (x² - 16x + 64) (x² - 8x - 8x + 64) = (x - 8)² (x² - 15x + 36) (x² - 12x - 3x + 36) = Is not a sp. product. A trinomial with first & third term squares is only a PST if... 9y3 + 12x2 + 4x PST or no PST?
- 4. Steps in factoring completely: 1. Look for the GCF 2. Look for special cases. a. difference of two squares b. perfect square trinomial 3. If a trinomial is not a perfect square, look for two different binomial factors. 8t4 – 32t3 + 40t = 8t(t3 - 4t + 5) 4x2 – 9y2 = (2x)2 – (3y)2 x2 + 8x + 16 = x2 + 8x + 42 = (x + 4)2 x2 + 11x – 10 = (x + 10)(x – 1)
- 5. An organized approach to factoring 2nd degree trinomials 5 Factoring (ax2 + bx + c) Trinomials
- 6. Factoring Trinomials Use this algorithm (procedure) to take the guesswork out of factoring trinomials. It would be a good idea to write the steps down once, as they are easy to forget when away from class You can use these steps for any ax2 + bx + c polynomial, and for any polynomial you are having difficulty factoring.
- 7. Step 1 7 Multiply the leading coefficient and the constant term
- 8. Step 2 8 Find the two factors of 24 that add to the coefficient of the middle term. Notice the 'plus, plus' signs in the original trinomial. Factors of 24: 1 24 2 12 3 8 4 6 Our two factors are 4 & 6
- 9. Step 3 9 Re-write the original trinomial and replace 10x with 6x + 4x. 3x2 + 6x + 4x + 8 Step 4 Factor by Grouping
- 10. Step 5 10 Factor out the GCF of each pair of terms After doing so, you will have... Step 6 Factor out the common binomial, check that no further factoring is possible, and the complete factorization is..
- 11. 11 Practice(2) Factor: 6x3 + 14x2 + 8x Factor: 4x2 – 20x + 25
- 14. 9y3 + 12x2 + 4x Factor 3x5 – 243xFactor 2m2 – 20mn + 50n2 Factor 5x4y – 80x2y3 Factor 5x – 5y + ax - ay