Factoring lesson
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1) The document discusses factoring trinomials by going from expressions like "x + 4x + 3" back into binomials using factors. 2) It provides examples of factoring various trinomial expressions into binomials like (x + 3)(x + 1). 3) The objective is to teach learners how to factor trinomials into binomials using techniques like finding two numbers with a sum and product that match the coefficients.
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2) It provides examples and steps for multiplying a monomial by a monomial, monomial by a polynomial, binomial by binomial, and a polynomial by a polynomial with three or more terms.
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Feb 19
1. A test on polynomials will be held on Thursday covering adding, subtracting, multiplying, and dividing polynomials.
2. Test scores from additional tests will be posted with the lowest score being dropped. Weekly Khan Academy grades for the first two weeks of the third quarter will be posted after Wednesday.
3. The new scoring schedule for Khan Academy assignments is 4 points for each correct answer, with 8 consecutive correct answers earning 100% and 7 out of 8 correct earning 28%. No credit will be given for questions where hints are used.
March 7
1. The document discusses factoring perfect square trinomials, which are polynomials where the first term is a perfect square, the third term is a perfect square, and the coefficient of the second term is twice the square root of the product of the first and third term coefficients.
2. To factor a perfect square trinomial, take the square root of the first term, add it to the square root of the third term, and place it in parentheses twice to get the two factors.
3. Examples are provided of determining if a trinomial is a perfect square and factoring perfect square trinomials like x2 + 10x + 25 as (x + 5)2.
Chapter 2.5
The document discusses the distributive property and combining like terms in algebra. It defines key terms such as terms, coefficients, and like terms. It then explains the distributive property using examples of distributing a number over terms in parentheses. Finally, it provides practice problems for students to work through using the distributive property to combine like terms.
Pc 9-5.ppt
The document discusses the binomial theorem and expanding binomial expressions. It introduces Pascal's triangle as a way to determine the coefficients in binomial expansions. Examples are provided of expanding expressions like (x + y)n, (x - 2y)4, and finding specific terms like the 6th term in the expansion of (3a + 2b)12. Formulas are given for determining the coefficients using binomial coefficients.
9.9
The document provides examples of factoring polynomials completely. It begins by outlining guidelines for factoring polynomials completely, such as factoring out the greatest common monomial factor, looking for differences of squares or perfect square trinomials, and factoring trinomials and polynomials with four terms by grouping. It then works through examples of factoring various polynomials completely by applying these guidelines. These include factoring trinomials, solving a polynomial equation, and solving a multi-step problem involving factoring a polynomial to find dimensions.
February 12
This document provides an overview of polynomials, including:
1. What a typical polynomial looks like, with a leading coefficient and terms in descending order of variables' exponents.
2. Polynomial basics, such as only adding or subtracting like terms. Methods for adding, subtracting, and multiplying polynomials are described.
3. The FOIL method for multiplying binomials is introduced, and the general rule that each term in one polynomial is multiplied by each term in the other. Exponents with like bases are added when multiplying terms. Examples of multiplying different types of polynomials are provided.
Day 3 subtracting polynomials
This document provides examples and instructions for subtracting polynomials. It begins with examples of subtracting terms like x+7 and 3x+9. It then shows how to subtract polynomials by removing common terms and combining like terms, such as (3x^2 + x + 2) - (2x^2 - x + 3). The document ends with homework assignments involving subtracting various polynomials.
Module 1 polynomial functions
This module introduces polynomial functions of degree greater than 2. It covers identifying polynomial functions from relations, determining the degree of a polynomial, finding quotients of polynomials using division algorithm and synthetic division, and applying the remainder and factor theorems. The document provides examples and practice problems for each topic. It aims to teach students how to work with higher degree polynomial functions.
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Factoring lesson
- 1. Intro Video: https://www.youtube.com/watch?v=wPOgvzVOQig
- 2. Last week: FOIL Method 1) First. Multiply the first terms in each binomial 2) Outer. Multiply the outer terms in each binomial 3) Inner. Multiply the inner terms in each binomial 4) Last. Multiply the last terms in each binomial **combine any like terms (x + 7)(x + 4) (x - 5)(x - 6)
- 3. review: (x + 5)(x - 3) (x - 3)(x - 3)
- 4. SHORT CUT! - 1st term: if both x's have a coefficient and power of 1, just put "x" - 2nd term: add both constants together, then add x - 3rd term: multiply both constants (x + 5)(x + 5) (x - 6)(x - 6)
- 5. This week: FACTORING!
- 6. (x + 3)(x + 1) x + 4x + 3 2
- 7. Objective: go from a trinomial back to binomials x + 4x + 3 2 ( )( )
- 8. Objective: go from a trinomial back to binomials x + 4x + 3 2 ( )( )
- 9. x - 7x + 10 2
- 10. x + 7x + 12 2
- 11. x - 3x - 10 2
- 12. do this as a group: x + 6x + 5 2 x + 4x - 12 2 x - 9x + 18 2 x - 100 2
- 13. if you can factor this, you are a factoring ninja! x - 5x - 24 2 answer: (x - 8)(x + 3)