1 / 11

Factoring ax 2 + bx + c

Factoring ax 2 + bx + c. 3x ² + 5x - 2. This is a little harder. I would start with the “first”: (3x )(x ) Your “last” needs to multiply to give you a -2 (#’s will have different signs)

orli
Download Presentation

Factoring ax 2 + bx + c

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. Factoring ax2 + bx + c

  2. 3x² + 5x - 2 • This is a little harder. • I would start with the “first”: (3x )(x ) • Your “last” needs to multiply to give you a -2 (#’s will have different signs) • Place them in a way that your “outside” and “inside” combine to get 5. • OR • Now multiply “a” and “c” (3 and –2). You get negative six. • Your “outside” answer and your “inside” answer multiply to get negative six AND combine (subtract because the signs must be different) to get 5. Try 6 and –1. • You must place numbers so that the “inner” and “outer” products will be 6 and –1. • (3x - 1)(x + 2)

  3. 3x2 – 19x + 20 • Factor Answer: (3x – 4)(x – 5)

  4. 8x2 + 27x + 9 • Factor: Answer: (8x + 3)(x + 3)

  5. Another Way—The Box • When factoring trinomials, you could use the box again. • Put the first term in the top left of a 2 by 2 box. • Put the last term in the bottom right square. • Multiply them (“a” and “c”) together. That is your “magic number”. • In f1= in the calculator, enter your magic number (#) f1 = #/x • In f2 = #/x + x

  6. Another Way—The Box • Go to the table. In the f2 column find the “b” number (the middle term). • In the two remaining boxes, enter the numbers next to that “b” number (the numbers in the “X” column and the y1 column). Be sure to put an x after each number. • Going across the top row find the GCF. Write it to the left of the box. • Then find the GCF of the bottom row and write it to the left of the box.

  7. Another Way—The Box • Then find the GCF of the first column and write it above that row. • Last find the GCF of the second column and write it above that row. • You now have the binomial factors of this trinomial.

  8. Example 1 • Factor 6x² + 13x – 5 • Multiply them to get the magic number. • Now enter in f1 -30/x • In f2 enter -30/x + x

  9. Example 1 • Go to the table and look in the f2 column and look for 13. • It is next to the 15 and –2 • So, write 15x and –2x in the remaining boxes.

  10. Example 1 • Find the GCF of each row and write it next to the row. • Find the GCF of each column and write it above the column. So it is (2x + 5)(3x – 1)

  11. Try these… Factor each trinomial. Check your answer. 1. 5x2 + 17x + 6 2. 2x2 + 5x – 12 3. 6x2 – 23x + 7 4. 4x2 - 11x - 20 5. 2x2- 7x + 3 (5x + 2)(x + 3) (2x– 3)(x + 4) (3x– 1)(2x– 7) (x - 4)(4x + 5) (2x - 1)(x - 3)

More Related