I need to develop these two question: l) (2x + 3)(x - 9) ll) -4(x +2)² I also need to factorize these two: l) -x² -2x + 35 ll) 3x² - 75 I don't understand either one, so if you could also explain how you get the answer, that would be great so I can use this as an example in the future Many thanks!
example of develop. This is algebra, so idk how you learn to do it but i would use FOIL F- first ( multiply the first numbers in each) O- outer (mulitply the numbers farthest away from eachother) I- inner (multiply the numbers closest to eachother) L- Last (multiply the last number in each bracket) So (2x + 3) (x - 9) F ..... 2x * x = 2x^2 O ..... 2x * -9 = -18x I ...... 3 * x = 3x L ..... 3 * 9 = 27 lay out into one equation (put + for the postive ones and - for the negative ones) like so: 2x^2 - 18x + 3x + 27 (put together common variables) 2x^2 (-18x + 3x) + 27 2x^2 -15x + 27 And thats your answer.
Sometimes things are best without accompanying text. Use the following solution progression as a supplement to the above explanation. l) (2x + 3)(x - 9) = 2x2 -18x +3x -27 = 2x2 - 15x - 27 ll) -4(x +2)² = -4(x+2)(x+2) = -4(x2+2x+2x+4) = -4(x2+4x+4) = -4x2 - 16x - 16 lol@ "factorize," feel free to just say "I need to factor these" l) -x² -2x + 35 In general its not good to have a negative leading coefficient. Factor out a negative sign: -(x2 +2x -35) You need a pair of numbers which multiply to negative 35 and add to 2. 1, -35 -1, 35 5, -7 -5, 7 7 and -5 work: -(x+7)(x-5) Solutions are -7 and 5 (where either binomial is equal to zero) ll) 3x² - 75 As was the case in the precious problem, where the leading coefficient was -1, we had problems. Just like in the last problem, let's factor out something from the expression so that the x^2 term has a coefficient of 1: 3(x2 - 25) Here you have an expression of the form (x2 - a2), where a is some number (in this case 5, since 5^2 =25). This is one of those handy dandy circumstances that you need to memorize: (x2 - a2) = (x + a)(x - a) So your factored expression is: 3(x-5)(x+5) Solutions are 5 or -5
I could help you add my msn I will solve them on a paper, upload on imageshack and send u the link on msn.
If you need any further help add me on MSN - I love factors, quadratics, and things along those lines. :0
