Myp7 multiply terms
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This document provides instructions and examples for multiplying algebraic terms. It explains that to multiply terms, you multiply the numbers and find the power when multiplying the same letter. When multiplying different letters, you write them together. The document also contains an example of multiplying terms of mixed sign and puts the steps together. It concludes by assigning practice problems and homework.
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2) Permutations of n objects taken r at a time is n!/(n-r)!.
3) Distinguishable permutations when some objects are alike uses the formula n!/(p!q!r!...).
4) Circular permutations (arranging objects in a circle) is (n-1)!. Examples and solutions are provided to illustrate each type of permutation.
AA Section 5-3
The document provides examples for solving systems of equations by substitution. It includes worked examples showing the step-by-step process of solving systems with 2-3 equations by substituting values from one equation into another and solving for the variables. The examples determine the number of different types of tickets (adult, student, children's) printed for a school play given the total number of tickets and relationships between the ticket amounts.
0303 ch 3 day 3
This document discusses finding the rational zeros of polynomials using the Rational Zeros Theorem. It provides examples of finding all rational zeros of polynomials by considering possible values of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. It also discusses using synthetic division and the Quadratic Formula to find the exact zeros of polynomials when not all zeros are rational.
Multiplying Polynomials
1) The document discusses multiplying different types of polynomials, including: monomials, binomials, and polynomials with more than two terms.
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.
3) The key steps are distributing terms, applying rules like the distributive property, and combining like terms in the results.
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.
January 23
Steps are shown for solving systems of equations by the elimination method, including multiplying one equation by a constant to eliminate a variable before adding the equations. Examples are provided of solving systems by substitution, where one variable is solved for in one equation and substituted into the other equation. Practice problems are given for students to apply
Dividing polynomials
1) The document explains various methods for dividing and factoring polynomials, including: dividing polynomials using long division; using Ruffini's rule to divide polynomials; applying the remainder theorem and factor theorem; and factoring polynomials through finding common factors, using identities, solving quadratic equations, and finding polynomial roots.
2) Specific factorization methods covered are removing common factors, using identities like a^2 - b^2, factoring quadratic trinomials, using the remainder theorem and Ruffini's rule to find factors for polynomials of degree greater than two, and identifying irreducible polynomials.
3) Additional algebraic identities explained are for cubing binomials like (a ± b)^3 and taking the square of trinomial
Index laws tutorial intermediate
This is a quick tutorial for students seeking to use the first, second and third index law at a more intermediate level.
3. Polynomials
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- 2. 3x × 2 y 3x × 2 y = 3 × 2 × x × y = 6 xy Multiply the numbers, and then multiply the letters
- 3. POWERS - EXPONENT x× x = x 2 x ×x = x 3 4 x ×x = x 3 5 8 p × q × r × p = p 4q 2r 2 3
- 4. NUMBERS AND LETTERS 3×y 5 x 2×x = 2 × xy 3 × x × ×5 × =0 x × 3× y2 =0 y 3x2
- 5. TERMS OF MIXED SIGN − × ×q 4 2 − p y 5 =× −p × −2 5 × y 4 ×× q = ××× 4 pqy 0 = 0q 4py
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