X-box Factoring Warm-Up Please complete these individually. 1. Fill in the following X-solve problems. a. b. 4 7 c.
15 36 10 13 2. Write the general form of a quadratic equation. 3. Divide using the box method. a. 4a3 + 12a2 + 6a 2a b. 14x5y3 35x4y2 + 21x2y 7xy
X- Box Product 3 -9 Sum X-box Factoring This is a guaranteed method for factoring quadratic equationsno guessing necessary! We will learn how to factor quadratic equations using the x-box method Background knowledge needed: Basic x-solve problems General form of a quadratic equation
Dividing a polynomial by a monomial using the box method Standard 11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Objective: I can use the x-box method to factor non-prime trinomials. Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)=
-30 2 -15 x -5 3x 3x2 -15x +2
2x -10 -13 3x2 -13x -10 = (x-5)(3x+2) Factor the x-box way y = ax2 + bx + c First and Last Coefficients Produ ct GCF
ac=mn n m Middle b=m+ Height n Sum Base 1 Base 2 1st Term
Factor n Factor m Last term Examples Factor using the x-box method. 1. x2 + 4x 12 a) b) x
-12 6 -2 4 x -2 x 2 + 6x 6
-2x -12 Solution: x2 + 4x 12 = (x + 6)(x - 2) Examples continued 2. x2 - 9x + 20 a) 20 -4 -5 -9 b)
x x -4 x2 -4x -5 -5x 20 Solution: x2 - 9x + 20 = (x - 4)(x - 5) Think-Pair-Share 1. Based on the problems weve done, list the steps in the diamond/box factoring method so that someone else can do a problem using only your steps. 2. Trade papers with your partner and
use their steps to factor the following problem: x2 +4x -32. Trying out the Steps 3. If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partners paper back to him. 4. Modify the steps you wrote to correct any incomplete or incorrect steps. Finish the problem based on your new steps and give the steps back to your partner. 5. Try using the steps again to factor: 4x2 +4x -3. Stepping Up 6. Edit your steps and factor:
3x2 + 11x 20. 7. Formalize the steps as a class. Examples continued continued 3. 2x2 - 5x - 7 a) -14 -7 2 -5 2x b) x
Jean Robert Argand, 18.7.1768. Geneva - 13.8.1822. Paris 1820 Cauchy u svojoj Cours d'analyse posvećuje čitavo poglavlje Argandovom dokazu, bez da ga spomene Gauss daje jedan nepotpun dokaz 1799, zatim dva potpuna dokaza 1816 Hermann Grassmann, 15.4.1809.
Mouth (oral or buccal cavity) Divided into: Vestibule - bounded externally by cheeks and lips and internally by gums and teeth. Oral cavity proper - extends from gums and teeth to fauces (the opening between oral cavity and pharynx) Cheeks...
However, if the economic value is evidence of mutual mistake, duress, undue influence, or fraud, the contract could be declared unconscionable (grossly unfair or oppressive) and may not be enforceable. ... Existing Duties. Settlement of Liquidated Debts.
Georgia's Geographic Regions. Essential Question??? What are the significant geographic regions of Georgia, and how have they impacted Georgia's growth and development? Georgia. Location. Between 30 - 35 Degrees North Latitude. Between 81 - 85 Degrees West Longitude .
2. REVENUE BEFORE COST. 3. THERE ARE NO OTHER RULES. (*5-year study/Deloitte: From a database of over 25,000 companies from hundreds of industries covering 45 years, the authors uncovered 344 companies that qualified as statistically "exceptional," and finally winnowed the...