1 / 14

SLIDE SHOW INSTRUCTIONS This presentation is completely under your control.

SLIDE SHOW INSTRUCTIONS This presentation is completely under your control. This lesson will show only one step at a time, to see the next step you must press a key. (Actual names written on a key are in green ) TO STOP THE SLIDE SHOW : press ‘escape’ ( Esc , top left of keyboard)

sauda
Download Presentation

SLIDE SHOW INSTRUCTIONS This presentation is completely under your control.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SLIDE SHOW INSTRUCTIONS • This presentation is completely under your control. • This lesson will show only one step at a time, • to see the next step you must press a key. • (Actual names written on a key are in green) • TO STOPTHE SLIDE SHOW: press ‘escape’ (Esc, top left of keyboard) • TO MOVE FORWARD: press the “spacebar” or Enter • (PageDn,  , , also work) • TO MOVE BACKWARD: press the  key • (PageUp, or also work)

  2. Factoring Formulas • Difference of Two Squares • Cube Formulas • Trinomials: x2+bx+c • or x2+bxy+cy2 • 4. Perfect Square Trinomials

  3. a b Answer Difference of Two Squares Use the formula: a2 - b2 = (a + b)(a - b) 1. Find a and b by taking the square root of each term. Example:x2 – 9 2. Place the numbers into the formula in the correct locations (x)2 - (3)2 = (x + 3)(x - 3) (replace the letter “a” in the formula with an “x”, replace the letter “b” with a “3”)

  4. a b Answer Difference of Two Cubes Use the formula: a3 – b3 = (a - b)(a2 + ab + b2) 1. Find a and b by taking the cube root of each term. Example:x3 – 8 2. Place the numbers into the formula in the correct locations (x)3 - (2)3 = (x - 2)(x2 + 2x + 4) (replace the letter “a” in the formula with an “x”, replace the letter “b” with a “2”)

  5. a b Answer Sum of Two Cubes Use the formula: a3 + b3 = (a + b)(a2 - ab + b2) 1. Find a and b by taking the cube root of each term. Example:x3 + 27 2. Place the numbers into the formula in the correct locations (x)3 + (3)3 = (x + 3)(x2 - 3x + 9) (replace the letter “a” in the formula with an “x”, replace the letter “b” with a “3”)

  6. Practice Problems: (Hit enter to see the answers) Factor using the correct formula 1) x2 - 16 5) 27 + 8t3 2) a3 + 8 6) y2 + x2 3) 4x2 - 1 7) 9b2 - 4 4) x3- a3 8) 64x3- a3 Answers: 1) (x + 4)(x - 4) 2) (a + 2)(a2 - 2a + 4) 3) (2x + 1)(2x - 1) 4) (x - a)(x2+ ax + a2) 5) (3 + 2t)(9 - 6t + 4t2) 6) y2+ x2 (it doesn’t factor) 7) (3b + 2)(3b - 2) 8) (4x - a)(16x2+ 4ax + a2)

  7. Trinomial of the form: x2 + bx + c 3. Make sure you have the correct signs: +2 and +4 = +6 1. Factor the last term: 2. Pick the pair or factors that when added together give you the middle term 1 + 8 = 9 2 + 4 = 6 1 * 8 2 * 4 4. Write these two numbers with an “x” in parentheses as follows, Answer: (x + 2)(x + 4) x2+ 6x+8 8

  8. Trinomial of the form: x2 + bx - c 3. Make sure you have the correct signs: +3 and -2 = +1 1. Factor the last term: 2. Pick the pair or factors that when subtracted give you the middle term 6 - 1 = 5 3 - 2 = 1 1 * 6 2 * 3 4. Write these two numbers with an “x” in parentheses as follows, Answer: (x + 3)(x - 2) x2+ x-6 6

  9. Trinomial of the form: x2 + bxy + cy2 3. Make sure you have the correct signs: +2 and +1 = +3 1. Factor the last term: (the coefficient only) 2. These factors when added together give you the middle term:1 + 2 = 3 1 * 2 4. Write these numbers with an “x” in the first position and a “y” in the second Answer: (x + 2y)(x + 1y) x2+ 3xy+ 2y2 2

  10. Practice Problems: (Hit enter to see the answers) Factor these polynomials 1) x2 + 3x - 10 2) x2 + 2x - 3 3) a2 - 6a - 7 4) x2 - 5xy + 6y2 5) y2 - 5y - 6 6) 9 +6y + y2 Answers: 1) (x + 5)(x - 2) 2) (x + 3)(x - 1) 3) (a + 1)(a - 7) 4) (x - 3y)(x - 2y) 5) (y - 6)(y + 1) 6) (3 + y)(3 + y) Note: On problem #6, you can put the terms in the correct order before you try to factor them.

  11. Perfect Square Trinomials +2ab a a2 b b2 (x + 3)2 = (x)2 + 2(x)(3) + (3)2 Formula (addition version): (a + b)2 = a2 + 2ab + b2 Find the product of (x + 3)2by plugging a and b into the formula (replace the letter a in the formula with x, and letter b with 3) = x2 + 6x + 9

  12. +2ab a a2 b b2 (x - 5)2 = (x)2 - 2(x)(5) + (5)2 Perfect Square Trinomials Formula (subtraction version): (a - b)2 = a2 - 2ab + b2 Find the product (x - 5)2by plugging a and b into the formula (replace the letter a in the formula with x, and letter b with 5) = x2 - 10x + 25

  13. Practice Problems: (Hit enter to see the answers) Use the correct formula to find the polynomial 1) (2x - 3)2 2) (a + 7)2 3) (4 - 2y)2 4) (x - y)2 Answers: 1) 4x2 -12x + 9 2) a2 + 14a + 49 3)16 - 16y + 4y2 4) x2 - 2xy + y2

  14. End of Tutorial Go to www.greenebox.com for more great math tutorials for your home computer Questions? send e-mail to: lgreene1@satx.rr.com

More Related