Investigation: Common Factors

Investigation: Common Factors

Today we are going to use the TI – Inspire calculators to explore Common Factors.

Factors are algebraic expressions written as the product of two or more algebraic expressions. Factoring is the “opposite” to expanding.

1. After opening a New Document (c + 6: New Document), insert a Calculator page. /
2. You can type in the word factor or access it through menus. (b > 4: Algebra > 2: Factor) Type in the expression you would like to factor. /
3. Press · to factor. /

Common Factoring

Table 1. Factor using your calculator.

a) 3x2 + 6x + 9 = ______/ b) 9x2 + 18x + 27 = ______
c) 7x2 + 14x + 21 = ______/ d) 5x2 + 10x + 15 = ______
Look at the questions you have completed. Look for a pattern. What is the pattern that you have observed?
Use this pattern to complete the next two questions. Check with your calculator.
e) 4x2 + 8x + 12 = ______/ f) 2x2 + 4x + 6 = ______

Table 2. Factor using your calculator.

a) x2 + x = ______/ b) x + x3 = ______
c) x2 + x3 = ______/ d) x3 + x2 = ______
Look at the questions you have completed. Look for a pattern. What is the pattern that you have observed?
Use this pattern to complete the next two questions. Check with your calculator.
e) x3 + x = ______/ f) x6 + x5 = ______

Table 3. Factor using your calculator.

a) 3x2 + 6x = ______/ b) 9x3 + 18x2 = ______
c) 7x3 + 14x2 = ______/ d) 5x2 + 10x3 = ______
Look at the questions you have completed. Look for a pattern. What is the pattern that you have observed?
Use this pattern to complete the next two questions. Check with your calculator.
e) 2x2 + 4x = ______/ f) 4x3 + 8x2 = ______

Describe in your own words: How do you factor a polynomial expression using common factoring?

Extra Practice!

(Try these on your own, and check using the graphing calculator).

1. 3x + 6 2. 9x + 3 3. 12x3 + 4x

4. 18x2 + 2x3 5. 60x3 – 30 6. 40x – 28

7. 2x2 + 60x + 20 8. 20x2 – 120 9. 35x3 + 7x