1 / 10

Comprehensive Guide to Factoring Quadratic Expressions

Learn how to factor quadratics, recognize difference of squares, identify perfect squares, and solve factoring problems with examples. Practice exercises included to enhance understanding.

jcherish
Download Presentation

Comprehensive Guide to Factoring Quadratic Expressions

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 Quadratic Expressions Objectives: Factor a difference of squares. Factor quadratics in the form Factor out the GCF. Factor quadratics with a GCF.

  2. Definitions Greatest Common Factor – the biggest number that will divide all terms evenly. If there are variables, the lower exponent is in the GCF. examples: Find the GCF 1) 9, 12

  3. Class Work Find the GCF: 1) 18, 20 2) 12, 24, 30 3) 4x, 20x 4) x2, 6x 5) 27x2, 36 6) 5x2, 6xy 7) 3y, 8x 8) 2x3, 3x2 9) 36a4, 72a2

  4. Factor out the GCF 1) x2 – 9x 2) 3x2 – 18x 3) 12x3 – 18x2 4) 2x2 + 4x + 10

  5. Recognizing a Difference of Squares There are ONLY two terms in the problem. It MUST be a minus sign in the middle. BOTH terms are perfect squares This is an example of a difference of squares 4x2 - 25

  6. Perfect Squares 9 is a perfect square because 3 x 3 = 9 36 is a perfect square because 6 x 6 = 36 81 is a perfect square because 9 x 9 = 81 12 is NOT a perfect square because there is no number times itself that will give you 12.

  7. Circle the Perfect Squares 16, 36, 20, 121, 144, 60, 50, 4, 225 9x2, 10x2, 81x3, 100x2, 44x2, 1000x4, 30x2

  8. Now you try…Factor: 1) x2 – 4 2) x2 - 81 3) 4x2 – x 4) 25x2 – 9 5) 100x4 – 49 6) 49x2 - 1 8) 4x2 + 25 9) 121x2 – 81y2

  9. Factoring Polynomials in the Formax2 + bx - c Factor: 1) x2 – 14x – 32 2) x2 + 13x + 22 3) x2 + 15xy + 14y2 4) x2 + 7x – 12 5) 6x2 + 13x + 2 6) 10x2 – 13x + 4

  10. Factoring Problems with a GCF 1) 4x2 – 16x – 48 2) 6x2 – 42x + 36 3) 2x2 + 46x – 100 4) x3 – 4x 5) 6x2 + 13x + 2 6) 6x2 – 6x - 72

More Related