Polynomial Division
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This document discusses various techniques for solving polynomial expressions using long division. It provides examples of: 1) Dividing polynomials with common variables and subtracting exponents 2) Simplifying polynomial expressions using factoring or long division 3) Dividing polynomials where one term is missing by treating the missing term as zero 4) Using long division to solve word problems involving areas of shapes
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Function
FUNCTION
A function is a set of ordered pairs which relates two sets such that to each element of one set there is only one element of the second set
Quadraticfunctionpresentation 100127142417-phpapp02
The document defines quadratic functions and discusses their various forms, including general, vertex, and factored forms. It also covers solving quadratic equations using methods like the quadratic formula, factoring, and completing the square. Additionally, it discusses key features of quadratic graphs like x-intercepts, y-intercepts, the vertex, and concavity. Examples are provided to illustrate finding these features and graphing parabolas.
Solution 3
The document provides the steps to solve a multi-part calculus problem involving derivatives, tangent lines, and circles. It determines the derivative of two functions f(x) and g(x), finds the equations of the tangent lines at specific x-values, identifies the intersection points of the tangent lines, and uses those intersection points as the centers of three circles with a radius of 5 to write the equations of the circles.
Algebra Revision.ppt
This document provides an overview of topics covered in intermediate algebra revision including: collecting like terms, multiplying terms, indices, expanding single and double brackets, substitution, solving equations, finding nth terms of sequences, simultaneous equations, inequalities, factorizing common factors and quadratics, solving quadratic equations, rearranging formulas, and graphing curves and lines. The document contains examples and practice problems for each topic.
March 6, 2014
Light can travel 186,000 miles in one minute. In scientific notation, this is 1.86x105 miles.
The document discusses multiplying polynomials and binomials. It introduces the box method and the F.O.I.L (First, Outer, Inner, Last) method for multiplying binomials. F.O.I.L involves distributing the first term of one binomial with each term of the other binomial. The sign of the middle and last terms depends on whether the signs of the last terms of each binomial are the same or different.
Extra Help 19- differential equations.pptx
This document provides information about solving first-order differential equations. It discusses the order of differential equations and gives examples of first-order equations. It also describes methods for solving separable and exact first-order differential equations, including separating variables, integrating, and finding particular solutions given initial conditions. Solving differential equations may require integration techniques like substitution, parts, and trigonometric identities.
Straight-Line-Graphs-Final -2.pptx
This document contains 5 math problems involving factorizing expressions, solving equations, evaluating expressions for given values, expanding expressions, and finding the highest common factor. It also provides context on working with straight line graphs, including finding the gradient and y-intercept of a line from its equation, finding the gradient between two points, finding the midpoint and a point that divides a line segment in a given ratio, and finding the x- and y-intercepts of a line.
Quadraticequation
A quadratic equation is a second-order polynomial with terms up to x^2. It has two roots, or solutions, which may be real or complex. The quadratic formula can be used to find the exact numeric values of the roots. A root is a value that makes the quadratic equation equal to zero. A double root occurs when the two roots are equal, making the quadratic a perfect square trinomial.
7.1 area between curves
The document discusses calculating the area between two curves. It explains that this area is defined as the limit of sums of the areas of rectangles between the curves as the number of rectangles approaches infinity, which is represented by a definite integral. It provides examples of finding the area between curves defined by various functions through setting up and evaluating the appropriate definite integrals.
7.1 area between curves
The document discusses calculating the area between two curves. It explains that this area is defined as the limit of the sum of the areas of rectangles between the curves as the number of rectangles approaches infinity, which is represented by a definite integral. It provides examples of finding the area between curves defined by various functions through setting up and evaluating the appropriate definite integral.
Quadratic equations
This document discusses quadratic equations and methods for solving them. It begins by defining quadratic equations as second degree polynomial equations of the form ax^2 + bx + c = 0, where a is not equal to 0. It then presents several methods for finding the roots or solutions of quadratic equations: factoring, completing the square, and using the quadratic formula. Examples are provided to illustrate each method. The document also discusses graphing quadratic functions and key features of parabolas such as vertex, axis of symmetry, and direction of opening.
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Information and Communication Technology in Education
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Polynomial Division
- 1. Dividing the same variable when you divide two terms with a common variable. You subtract the exponent of the division. Ex) x ³ x² = x³-² = x Ex) (2x³ + 4x² + 6x) 2x = 2x³ + 4x² + 6x 2x 2x 2x = 2x² + 2x + 3 Anything to the power of zero is always one