Dividing Polynomials Using Synthetic Division. List all coefficients (numbers in front of x's) and the constant along the top. If a term is missing, put.

Slides:

Advertisements

Similar presentations

RATIONAL FUNCTIONS A rational function is a function of the form:

Advertisements

Equations in Quadratic Form

< < < > > >         . There are two kinds of notation for graphs of inequalities: open circle or filled in circle notation and interval notation.

Operations on Functions

Solving Quadratic Equations.

Parallel and Perpendicular Lines. Gradient-Intercept Form Useful for graphing since m is the gradient and b is the y- intercept Point-Gradient Form Use.

LINES. gradient The gradient or gradient of a line is a number that tells us how “steep” the line is and which direction it goes. If you move along the.

If a > 0 the parabola opens up and the larger the a value the “narrower” the graph and the smaller the a value the “wider” the graph. If a < 0 the parabola.

PAR TIAL FRAC TION + DECOMPOSITION. Let’s add the two fractions below. We need a common denominator: In this section we are going to learn how to take.

Let's find the distance between two points. So the distance from (-6,4) to (1,4) is 7. If the.

REAL NUMBERS. {1, 2, 3, 4,... } If you were asked to count, the numbers you’d say are called counting numbers. These numbers can be expressed using set.

DOUBLE-ANGLE AND HALF-ANGLE FORMULAS

(r,  ). You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate system called the polar coordinate.

SPECIAL USING TRIANGLES Computing the Values of Trig Functions of Acute Angles.

SOLVING LINEAR EQUATIONS. If we have a linear equation we can “manipulate” it to get it in this form. We just need to make sure that whatever we do preserves.

TRIGONOMETRIC IDENTITIES

You walk directly east from your house one block. How far from your house are you? 1 block You walk directly west from your house one block. How far from.

Logarithmic Functions. y = log a x if and only if x = a y The logarithmic function to the base a, where a > 0 and a  1 is defined: exponential form logarithmic.

INVERSE FUNCTIONS.

The definition of the product of two vectors is: 1 This is called the dot product. Notice the answer is just a number NOT a vector.

Dividing Polynomials.

exponential functions

GEOMETRIC SEQUENCES These are sequences where the ratio of successive terms of a sequence is always the same number. This number is called the common ratio.

VECTORS. A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude.

The standard form of the equation of a circle with its center at the origin is Notice that both the x and y terms are squared. Linear equations don’t.

A binomial is a polynomial with two terms such as x + a. Often we need to raise a binomial to a power. In this section we'll explore a way to do just.

ARITHMETIC SEQUENCES These are sequences where the difference between successive terms of a sequence is always the same number. This number is called the.

Properties of Logarithms

Logarithmic and Exponential Equations. Steps for Solving a Logarithmic Equation If the log is in more than one term, use log properties to condense Re-write.

A polynomial function is a function of the form: All of these coefficients are real numbers n must be a positive integer Remember integers are … –2, -1,

Library of Functions You should be familiar with the shapes of these basic functions. We'll learn them in this section.

SEQUENCES A sequence is a function whose domain in the set of positive integers. So if I gave you a function but limited the domain to the set of positive.

11.3 Powers of Complex Numbers, DeMoivre's Theorem Objective To use De Moivre’s theorem to find powers of complex numbers.

COMPLEX Z R O S. Complex zeros or roots of a polynomial could result from one of two types of factors: Type 1 Type 2 Notice that with either type, the.

Sum and Difference Formulas. Often you will have the cosine of the sum or difference of two angles. We are going to use formulas for this to express in.

Solving Quadratics and Exact Values. Solving Quadratic Equations by Factoring Let's solve the equation First you need to get it in what we call "quadratic.

Surd or Radical Equations. To solve an equation with a surd First isolate the surd This means to get any terms not under the square root on the other.

Algebraic long division Divide 2x³ + 3x² - x + 1 by x + 2 x + 2 is the divisor The quotient will be here. 2x³ + 3x² - x + 1 is the dividend.

COMPOSITION OF FUNCTIONS “SUBSTITUTING ONE FUNCTION INTO ANOTHER”

VECTORS. A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude.

Warm Up! Complete the square Quadratic Functions and Models.

Remainder and Factor Theorems. REMAINDER THEOREM Let f be a polynomial function. If f (x) is divided by x – c, then the remainder is f (c). Let’s look.

INTRODUCING PROBABILITY. This is denoted with an S and is a set whose elements are all the possibilities that can occur A probability model has two components:

The sum f + g This just says that to find the sum of two functions, add them together. You should simplify by finding like terms. Combine like terms &

Let's just run through the basics. x axis y axis origin Quadrant I where both x and y are positive Quadrant II where x is negative and y is positive Quadrant.

Dividing Polynomials. First divide 3 into 6 or x into x 2 Now divide 3 into 5 or x into 11x Long Division If the divisor has more than one term, perform.

We’ve already graphed equations. We can graph functions in the same way. The thing to remember is that on the graph the f(x) or function value is the.

The sum f + g This just says that to find the sum of two functions, add them together. You should simplify by finding like terms. Combine like terms &

(r,  ). You are familiar with plotting with a rectangular coordinate system. We are going to look at a new coordinate system called the polar coordinate.

Systems of Inequalities.

RATIONAL FUNCTIONS II GRAPHING RATIONAL FUNCTIONS.

Warm-up: Do you remember how to do long division? Try this: (without a calculator!)

THE DOT PRODUCT.

Matrix Algebra.

Absolute Value.

Graphing Techniques: Transformations Transformations Transformations

Warm-up: Divide using Long Division

Dividing Polynomials Using Synthetic Division

SIMPLE AND COMPOUND INTEREST

Dividing Polynomials © 2002 by Shawna Haider.

Solving Quadratic Equations.

Dividing Polynomials.

Symmetric about the y axis

exponential functions

Symmetric about the y axis

Graphing Techniques: Transformations Transformations: Review

Rana karan dev sing.

Presentation transcript:

Dividing Polynomials Using Synthetic Division

List all coefficients (numbers in front of x's) and the constant along the top. If a term is missing, put in a 0. 1 Set divisor = 0 and solve. Put answer here. x + 3 = 0 so x = - 3 Synthetic Division There is a shortcut for long division as long as the divisor is x – k where k is some number. (Can't have any powers on x) Bring first number down below line Multiply these and put answer above line in next column - 3 Add these up 3 Multiply these and put answer above line in next column - 9 Add these up Multiply these and put answer above line in next column Add these up This is the remainder Put variables back in (one x was divided out in process so first number is one less power than original problem). x 2 + x So the answer is:

List all coefficients (numbers in front of x's) and the constant along the top. Don't forget the 0's for missing terms. 1 Set divisor = 0 and solve. Put answer here. x - 4 = 0 so x = 4 Let's try another Synthetic Division Bring first number down below line Multiply these and put answer above line in next column 4 Add these up 4 Multiply these and put answer above line in next column 16 Add these up Multiply these and put answer above line in next column Add these up This is the remainder Now put variables back in (remember one x was divided out in process so first number is one less power than original problem so x 3 ). x 3 + x 2 + x + So the answer is: 0 x 3 0 x Multiply these and put answer above line in next column Add these up

List all coefficients (numbers in front of x's) and the constant along the top. If a term is missing, put in a 0. You want to divide the factor into the polynomial so set divisor = 0 and solve for first number. Let's try a problem where we factor the polynomial completely given one of its factors Bring first number down below line Multiply these and put answer above line in next column - 8 Add these up 0 Multiply these and put answer above line in next column 0 Add these up Multiply these and put answer above line in next column Add these up No remainder so x + 2 IS a factor because it divided in evenly Put variables back in (one x was divided out in process so first number is one less power than original problem). x 2 + x So the answer is the divisor times the quotient: You could check this by multiplying them out and getting original polynomial

Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar