College Algebra K/DC Wednesday, 23 September 2015 OBJECTIVE TSW factor polynomial expressions by (1) GCF, (2) grouping, and (3) trinomials. The tests are not graded.

College Algebra K/DC Thursday, 24 September 2015 OBJECTIVE TSW factor polynomial expressions by (1) GCF, (2) grouping, and (3) trinomials. The tests are not graded. TODAY’S ASSIGNMENT Sec. R.4: p. 38 (1-16 all, 19-24 all) Due tomorrow, Friday, 25 September 2015.

Factoring Polynomials Factoring Out the Greatest Common Factor ▪ Factoring by Grouping ▪ Factoring Trinomials

Example Factoring Out the Greatest Common Factor Factor out the greatest common factor from each polynomial. When factoring variables, factor the smallest exponent. (a) (b)

Example Factoring Out the Greatest Common Factor Factor out the greatest common factor from the polynomial. (c) This now needs to be simplified. GCF = 2(x – 2)

Example Factoring By Grouping Factor by grouping. First, group the terms into parentheses. Factor each individual parentheses. Now factor out the parentheses.

Example Factoring By Grouping Factor by grouping.

Example Factoring By Grouping Factor by grouping. . . . causing the next sign to switch. The middle term is negative . . .

Example Factoring (GCF and Grouping) Factor the expression.

Example Factoring (GCF and Grouping) Factor the expression (on your own).

Assignment: Sec. R.4: p. 38 (1-16 all, 19-24 all) Due on Friday, 25 September 2015. Use a separate sheet of notebook paper. This will be the last assignment for which you get a hard copy. R-11 11

College Algebra K/DC Friday, 25 September 2015 OBJECTIVE TSW factor (1) trinomials, and (2) differences of squares. ASSIGNMENT DUE (wire basket) Sec. R.4: p. 38 (1-16 all, 19-24 all) TODAY’S ASSIGNMENT (due on Tuesday, 09/29/15) Sec. R.4: pp. 38-39 (25-45 odd, 51-60 all) QUIZ: Factoring GCF, Grouping, Trinomials on Monday, 09/28/15.

Factoring Polynomials Factoring Trinomials ▪ Factoring Binomials – Differences of Squares

Example Factoring Trinomials (Guess and check Method) Factor , if possible. The positive factors of 5 are 5 and 1. The factors of –12 are –12 and 1, 12 and – 1, –6 and 2, 6 and –2, –4 and 3, or 4 and –3.

Example Factoring Trinomials (Guess and check Method) Try different combinations:

Example Factoring Trinomials (Box Method) Factor , if possible. Multiply 12 and –3. = –36 12t 2 –9t “Are there two factors of –36 that add up to –5?” 4t –3 1st: Put the squared term in the upper left, constant term in the lower right. 2nd: Multiply 12 and –3: –36. “Are there 2 factors of –36 that add up to –5?” 3rd: Yes, –9 and 4. Place these in the remaining two boxes (either order).

Example Factoring Trinomials (Box Method) Factor , if possible. 4t –3 3t 12t2 –9t 1 4t –3 4th: Factor each row and column. 5th: Write the answer: (3t + 1)(4t – 3)

Example Factoring Trinomials (Box Method) (3)(16) = 48 There are not two factors of 48 that equal –15.

Example Factoring Trinomials (Box Method) HINT: Is there a GCF? 4x 5 (8)(5) = 40 2x 8x2 10x Are there two numbers whose product is 40 and sum is 14? 1 4x 5 Don’t forget the 3!!!

Example Factoring Perfect Square Trinomials Factor each trinomial: (a) (b) Perfect square Positive perfect square Is the middle term 2(7x)(2y)? YES!

Factoring Differences of Squares REMEMBER: When factoring, ALWAYS look for a GCF 1st. Then, look for a pattern: 1. Are there four terms? If it factors, you’ll probably use grouping. 2. Are there three terms? If it factors, you’ll probably factor using guess and check or the box method.

Factoring Differences of Squares 3. Are there two terms? If there are, is the problem a difference (subtraction)? a. Are the two terms perfect squares? If they are, then use the pattern of differences of squares.

Factoring Differences of Squares If there is a GCF, factor it out first: Be careful: R-23

Example Factoring Differences of Squares Factor each binomial: (a) (b) (c)

Example Factoring Differences of Squares Sometimes, you may have to factor more than once. Always factor completely (factor until you can’t factor anymore)! R-25

Assignment (09/25/2015) Sec. R.4: pp. 38-39 (25-45 odd, 51-60 all) Write the problem and factor. Due Tuesday, 29 September 2015. QUIZ: Factoring GCF, Grouping, Trinomials on Monday, 09/28/15. R-26 26