1 College Algebra K/DC Tuesday, 16 September 2014 OBJECTIVE TSW add, subtract, mulitply, and divide polynomials. ASSIGNMENT CHANGE FOR TODAY –Sec. R.3: p. 31 (43-48 all, even, odd)

3-2 Polynomials R.3 Adding Polynomials ▪ Subtracting Polynomials ▪ Multiplying Polynomials ▪ Dividing Polynomials

2-3 Like Terms 4x 3 and  x 3 5b and 8b 10a 2 and 3a 2 5x 4 y 5 and  2x 4 y 5 Not Like Terms 4x 3 and  x 2 5b and 8ab 10a 2 and 2a 10 5x 5 y 4 and  2x 4 y 5 To add or subtract polynomials, add or subtract the coefficients of like terms. Like terms are terms with the same variables each raised to the same powers.

2-4 Adding and Subtracting Polynomials Add or subtract.

2-5 Adding and Subtracting Polynomials Add or subtract.

2-6 Adding and Subtracting Polynomials Add or subtract.

2-7 Adding and Subtracting Polynomials Add or subtract.

2-8 Multiplying Two Binomials (FOIL Method) Multiply F O I L

2-9 Squaring a Binomial (square the first term) – 2(first term)(second term) + (square the second term) Always positive Shortcut:

2-10 Squaring a Binomial

2-11 Multiplying Polynomials Find the product. Use FOIL.

2-12 Multiplying Polynomials Find the product. Notice that the two parentheses have the same terms; the only difference is that one is an addition and one a subtraction. This is a special product of two binomials called the difference of two squares. The two middle terms will always cancel. Memorize this pattern!!!

2-13 Multiplying Polynomials Multiply Technique #1: Distribution

2-14 Multiplying Polynomials Multiply Technique #2: Box Method I do not have a preference as to which method you use; you may use whichever is easiest for you. 3t23t2 –2t7 4t4t12t 3 –8t 2 28t –5–15t 2 10t–35

2-15 Multiplying Polynomials Find the product. Multiply the parentheses first. Then distribute.

2-16 Multiplying Polynomials Find the product: Product of the sum and difference of two terms.

2-17 Multiplying Polynomials Find the product: Rewrite as the product of two squares. Use the box method to multiply.

2-18 Multiplying Polynomials Find the product: HINT: Rewrite. Now use the box method to multiply.

Assignment: Sec. R.3 – p. 31 (43-48 all, even, odd) Due on Friday, 19 September Find each sum or difference. Find each product. Perform the indicated operation. 2-19

20 College Algebra K/DC Wednesday, 17 September 2014 OBJECTIVE TSW add, subtract, multiply, and divide polynomials. ASSIGNMENTS DUE FRIDAY (QUIZ Day) –Sec. R.3: p. 31 (43-48 all, even, odd) Yesterday’s assignment. –Sec. R.3: p. 31 (87-94 all) Today’s book assignment. –WS Sec. R.3 Today’s worksheet.

Dividing Polynomials One term in the denominator Create separate fractions and simplify.

Dividing Polynomials

More than one term in the denominator Use long division.

Dividing Polynomials 2-24

Dividing Polynomials 2-25 Placeholders for missing terms Stop! The degree of the remainder (1) Is less than the degree of the divisor (2).

Assignment Sec. R.3: p. 31 (87-94 all) –Due on Friday, 19 September 2014 (QUIZ day). WS Sec. R.3 –Due on Friday, 19 September 2014 (QUIZ day). Also due on Friday, 19 September 2014: –Sec. R.3: p. 31 (43-48 all, even, odd) 2-26

Assignment: Sec. R.3 – p. 31 (87-94 all) Due on Friday, 19 September Write each problem and perform each division. 2-27