Monday: Announcements This is last week for 3rd grading period Today’s assignments are the last grades Unit 7 Reassessment sign-ups on the round table. Deadline is Friday morning to reassess. Unit 8 is a 2 part unit (calculator and non-calculator) Afternoon tutorials this week start at 4:10pm because of teacher duty

Add, Subtract, Multiply, and Divide Polynomials Unit 8

Objectives I can add, subtract, and multiply polynomial expressions. I can divide polynomial expressions using Long Division

Polynomials A polynomial is a monomial or sum of monomials. The monomials that make up the polynomial are called terms of the polynomial. A trinomial has 3 unlike terms A binomial has 2 unlike terms

Standard Format

Standard Format

Addition and Subtraction Polynomials and monomials may only be subtracted or added if they have like terms. Addition and subtraction cannot be done on unlike terms. To add or subtract, you just COMBINE LIKE TERMS

Addition or Subtraction Simplify the following: (4x2 – 3x) – (x2 + 2x – 1) 4x2 – 3x – x2 - 2x + 1 3x2 – 5x + 1

Example #2 Simplify: (3x + y) – (x + y) – (x + 3y)

Example 3 Simplify (z2 – 6z – 10) + (2z2 + 4z – 11)

EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x3 – 5x2 + 3x – 9 and x3 + 6x2 + 11 in a vertical format. SOLUTION a. 2x3 – 5x2 + 3x – 9 + x3 + 6x2 + 11 3x3 + x2 + 3x + 2

GUIDED PRACTICE for Examples 1 and 2 Find the sum or difference. 1. (t2 – 6t + 2) + (5t2 – t – 8) SOLUTION t2 – 6t + 2 + 5t2 – t – 8 6t2 – 7t – 6

Multiply with Distributive Prop Simplify: 3x(5x4 – x3 + 4x) 15x5 – 3x4 + 12x2

2nd Example: (x + 3)(x2 + 3x + 9) x3 + 3x2 + 9x + 3x2 + 9x + 27

Example 3 Simplify: -3x2y(2x3y2 – 3x2y2 + 4x3y) -6x5y3 + 9x4y3 –12x5y2

Dividing Numbers Quotient When you divide a number by another number and there is no remainder: Then the divisor is a factor!! Also the quotient becomes another factor!!! Divisor Dividend

Dividing Polynomials Long division of polynomials is similar to long division of whole numbers. When you divide two polynomials you can check the answer using the following: dividend = (quotient • divisor) + remainder The result is written in the form: quotient + Dividing Polynomials

Dividing Polynomials Example: Divide x2 + 3x – 2 by x + 1 and check the answer. 1. x + 2 2. x2 + x 3. 2x – 2 2x + 2 4. – 4 5. remainder 6. Answer: x + 2 + – 4 Dividing Polynomials

Example: Divide & Check Example: Divide 4x + 2x3 – 1 by 2x – 2 and check the answer. x2 + x + 3 Write the terms of the dividend in descending order. 2x3 – 2x2 Since there is no x2 term in the dividend, add 0x2 as a placeholder. 2x2 + 4x 2x2 – 2x 1. 2. 6x – 1 4. 3. 6x – 6 5 5. Answer: x2 + x + 3 5 6. 7. 8. 9. Example: Divide & Check

Example: Division With Zero Remainder Example: Divide x2 – 5x + 6 by x – 2. x – 3 x2 – 2x – 3x + 6 – 3x + 6 Answer: x – 3 with no remainder. Example: Division With Zero Remainder

Homework WS 8-1