Divide a polynomial by a binomial

Slides:

Advertisements

Similar presentations

EXAMPLE 3 Standardized Test Practice SOLUTION 8x 3 y 2x y 2 7x4y37x4y3 4y4y 56x 7 y 4 8xy 3 = Multiply numerators and denominators. 8 7 x x 6 y 3 y 8 x.

Advertisements

Standard 10 add, subtract, multiply, and divide monomials and polynomials monomials are just one thing binomials are like bx + c polynomials are like ax².

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

EXAMPLE 2 Find a least common multiple (LCM)

EXAMPLE 1 Use polynomial long division

Evaluating Expressions Words - Algebra Adding & Subtracting Polynomials Multiplying and Dividing Polynomials Factoring (Smactoring)

Polynomials and Factoring Review By: Ms. Williams.

Polynomial Long Division. And we know that FACTORS help us find x intercepts and solutions! This is what we were using long division in grade school for….

EXAMPLE 3 Use synthetic division Divide f (x)= 2x 3 + x 2 – 8x + 5 by x + 3 using synthetic division. – – 8 5 – 6 15 – 21 2 – 5 7 – 16 2x 3 + x 2.

HW: Pg #13-61 eoo.

EXAMPLE 1 Multiply a monomial and a polynomial Find the product 2x 3 (x 3 + 3x 2 – 2x + 5). 2x 3 (x 3 + 3x 2 – 2x + 5) Write product. = 2x 3 (x 3 ) + 2x.

3.7 Warm Up Solve the equation. 1. √(x + 3) + 8 = √(8 – 3x) + 5 = √(2x + 1) – 7 = 1.

Dividing Polynomials Chapter – – 15y 4 – 27y 3 – 21y 2 3y – 27 3 – 21 3 y 2 y Divide. y 4 y 2 y 2 y 3 y 2 y 2 Write as separate fractions.

Do Now Pass out calculators. Write down the weeks assignments. Pick up a worksheet from the back and wait for instructions.

Warm Up Divide using long division ÷ ÷

3.7Divide Polynomials Example 1 Divide a polynomial by a monomial Divide 10x 3  25x x by 5x. Solution Method 1: Write the division as a fraction.

EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x – 3 ) Factor trinomial.

4.8b SKM & PP 1 Division of Polynomials. 4.8b SKM & PP 2 Division of Polynomials First, let’s review the symbols that represent the division problem:

HW: 6.2 Practice Worksheet. EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 – 5x 2 + 3x – 9 and x 3 + 6x in a vertical format.

Polynomial Terms and Operations. EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 – 5x 2 + 3x – 9 and x 3 + 6x in a vertical.

Multiply polynomials vertically and horizontally

SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x.

Multiplying Polynomials *You must know how to multiply before you can factor!”

Aim: How do we multiply polynomials? Do Now: Multiply the following 1. 2x(3x + 1) 2. (x – 1)(x + 2) 3. (x +2)(x 2 – 3x + 1)

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

Dividing Polynomials – Part 2 Honors Math – Grade 8.

8 4 Multiply & Divide Rational Expressions

Subtracting Polynomials

Prerequisite Skills VOCABULARY CHECK 40 ANSWER What is the least common denominator of and ? Which equation is a direct variation equation,

Dividing Polynomials. Simple Division - dividing a polynomial by a monomial.

Warm up Objective: To divide polynomials Lesson 6-7 Polynomial Long Division.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 4 Polynomials.

SOLUTION Divide a polynomial by a monomial EXAMPLE 1 Divide 4x 3 + 8x x by 2x. Method 1 : Write the division as a fraction. Write as fraction. Divide.

WARM UP 1. Factor the polynomial completely. 27 – y 3 2. What are the real number solutions of the equation 2x = x 2 + x 3 ?

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.

EXAMPLE 3 Multiply polynomials vertically

6.4 Multiplying/Dividing Polynomials 1/10/2014. How do you multiply 1256 by 13?

9.3 Simplifying and Multiplying Rational Expressions 4/26/2013.

EXAMPLE 4 Rewrite polynomials Divide 5y + y by 2 + y. Rewrite polynomials. Multiply y and y + 2. y 2 + 2y Subtract y 2 + 2y. Bring down 4. 3y + 4.

EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 – 5x 2 + 3x – 9 and x 3 + 6x in a vertical format. SOLUTION a. 2x 3 – 5x 2 + 3x.

Objective The student will be able to: multiply two polynomials using the distributive property.

Warm-Up Exercises Section 5.5 Adding and Subtracting Rational Expressions.

Chapter 5 Section 5. EXAMPLE 1 Use polynomial long division Divide f (x) = 3x 4 – 5x 3 + 4x – 6 by x 2 – 3x + 5. SOLUTION Write polynomial division.

Dividing Polynomials. Long Division of Polynomials Arrange the terms of both the dividend and the divisor in descending powers of any variable. Divide.

Warm-Up Exercises Perform the operation. 1. x x + 36 x 2 – x5x x 2 – 6x + 9 · x 2 + 4x – 21 x 2 + 7x ANSWERS x + 3 x – 12 ANSWERS 5 x – 3.

Factor the expression x – 5x2 3. x3 – 125 ANSWER 5x (2 – x)

11-3 Dividing Polynomials Hubarth Algebra. Divide (18x 3 + 9x 2 – 15x) by 3x 2. (18x 3 + 9x 2 – 15x)3x23x2 ÷= 1 3 x 2 = + – 18x 3 3x 2 9x23x29x23x2 15x.

Warm-Up Exercises ANSWER Find the least common multiple of 20 and Add ANSWER 4 5.

EXAMPLE 3 Multiply polynomials vertically and horizontally a. Multiply –2y 2 + 3y – 6 and y – 2 in a vertical format. b. Multiply x + 3 and 3x 2 – 2x +

#2.5 Long Division.

Do-Now Evaluate 7.1 × 104. Multiply (x2•y3•z4)•(x•y7•z2).

Monomials (Ex: 2x): It divides into everything…

Aim: How do we divide a polynomial by a binomial?

Dividing Polynomials.

Dividing Polynomials.

Solve a quadratic equation

Polynomial Long Division

Add, Subtract and Multiply Polynomials

Add and Subtract Rational Expressions

Dividing Polynomials.

Exponents and Polynomials

Dividing Polynomials.

Warm-Up Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Divide the number in C by 10.

Dividing Polynomials.

Section 5.6 Dividing Polynomials.

3.7 Divide Polynomials - + Divide a polynomial by a monomial = =

EXAMPLE 4 Solve proportions Solve the proportion. ALGEBRA a x 16

Presentation transcript:

Divide a polynomial by a binomial EXAMPLE 2 Divide a polynomial by a binomial Divide x2 + 2x – 3 by x – 1. SOLUTION STEP 1 Divide the first term of x2 + 2x – 3 by the first term of x – 1. x x – 1 x2 + 2x – 3 Think: x2 x = ? x2 – x Multiply x and x – 1. 3x Subtract x2 – x from x2 + 2x.

Divide a polynomial by a binomial EXAMPLE 2 Divide a polynomial by a binomial STEP 2 Bring down –3. Then divide the first term of 3x – 3 by the first term of x – 1. x – 1 x2 + 2x – 3 x2 – x 3x – 3 x + 3 Think: 3x x = ? 3x – 3 Multiply 3 and x – 1. Subtract 3x – 3 from 3x – 3. ANSWER (x2 + 2x – 3) (x – 1) = x + 3

Divide a polynomial by a binomial EXAMPLE 3 Divide a polynomial by a binomial Divide 2x2 + 11x – 9 by 2x – 3. x 2x2 –3x 14x – 21 + 7 2x – 3 2x2 + 11x – 9 Multiply x and 2x – 3. 14x – 9 Subtract 2x2 – 3x. Bring down – 9. Multiply 7 and 2x – 3. 12 Subtract 14x – 21. ANSWER (2x2 + 11x – 9) (2x – 3) = x + 7 + 12 2x – 3

GUIDED PRACTICE for Examples 2 and 3 Divide: (a2 + 3a – 4) (a + 1) a + 2 + ANSWER – 6 a + 1 Divide: (9b2 + 6b + 8) (3b – 4) ANSWER 3b + 6 + 32 3b – 4