1 / 5

F ACTORING A Q UADRATIC T RINOMIAL

F ACTORING A Q UADRATIC T RINOMIAL. To factor quadratic polynomials whose leading factor is not 1:. b = m q + p n. Find the factors of a ( m and n ). a = mn. Find the factors of c ( p and q ). a x 2 + b x + c = ( m x + p )( n x + q ). The sum of the outer and

zenda
Download Presentation

F ACTORING A Q UADRATIC T RINOMIAL

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 A QUADRATIC TRINOMIAL To factor quadratic polynomials whose leading factor is not 1: b = mq + pn Find the factors of a (m and n). a= mn Find the factors of c (p and q). ax2 + bx + c = (mx + p)(nx + q) The sum of the outer and inner products (mq + pn) is b. c= pq

  2. FACTORING A QUADRATIC TRINOMIAL 22 = 3 •4 + 5 •2 a= mn 6 = 3 • 2 c= pq 6x2 + bx + 20 = (3x + 5)(2x + 4) b = mq + pn c= pq

  3. One Pair of Factors for a and c Factor2x2 + 11x + 5 Test combinations of factors for SOLUTION a 1 and 2 c 1 and 5 Try a= 1 • 2 and c= 1 • 5 (1x + 1) (2x + 5) = 2x2 + 7x + 5 Not correct. Try a= 1 • 2 and c = 5 • 1 (1x + 5) (2x + 1) = 2x2 + 11x + 5 Correct.

  4. A Common Factor for a, b, and c Factor6x2 + 2x – 8 SOLUTION Begin by factoring out the common factor 2. The correct factorization is 6x2 – 2x – 8 = 2(x + 1)(3x – 4). 6x2 + 2x – 8 2 (3x2 – x – 4) = Now factor 3x2 – x – 4 by testing possible factors of a and c. FACTORS OFaANDc PRODUCT CORRECT? When you factor, you can stop testing once you find the correct factorization. a = 1 • 3 and c = (–2)(2) (x – 2)(3x + 2) = 3x2 – 4x – 4 No a = 1 • 3 and c = (2)(–2) (x + 2)(3x – 2) = 3x2 + 4x – 4 No (x – 4)(3x + 1) = 3x2– 11x – 4 a = 1 • 3 and c = (–4)(1) No Yes a = 1 • 3 and c = (1)(–4) (x + 1)(3x – 4) = 3x2 – x – 4

  5. Writing a Quadratic Model 3 2 The solutions are 2 and . – SOLVING QUADRATIC EQUATIONS BY FACTORING A cliff diver jumps from a ledge 48 feet above the ocean with an initial upward velocity of 8 feet per second. How long will it takeuntil the diver enters the water? SOLUTION Use a vertical motion model. Let v = 8 and s = 48. When the diver enters the water, h = 0. Solve the resulting equation for t. h= –16t2+vt+s Vertical motion model 0 = – 16t2 + 8t + 48 Write quadratic model. = – 16t2 + 8t + 48 Substitute values. 0 = (– 8)(2t2 – t – 6) Factor out – 8. 0 = (– 8)(t – 2)(2t + 3) Factor. Negative values do not make sense, so the only reasonable solution is t= 2. It will take the diver 2 seconds.

More Related