this is math homework. factoring trinomials?

[xoxomlw0813]

I know that i should be doing this on my own but i just seriously don't understand this. If any one will solve these problems for me I'll really appriciate it. This homework is 'factoring trinomials' it's 10th math.1. 6x² - x - 22. 10t² + t - 23. 9h² - 6h - 84. 6r² + 7r -105. 5a² -7ab -6b²6. 8x² -10xy - 25y²7.14m² +19mn - 3n²8. 18w² - z - 5z²9. 16h² +8hk -15k²10. 10x² - 25x -6011. 16p² -4pq - 30q²12. 42r² -3rt - 9t²13. 6c³ + 11c² -10c14. 4y² -13y -1215. 2d² +d -2116. 8m² -34m -9 17. 12f² +35f +8

[juxtapoz]

you just said it yourself, you should be doing this on your own...1. 6x² - x - 2= (2x+1)(3x -2)2. 10t² + t - 2= (2t+1)(5t -2)3. 9h² - 6h - 8= (3h+2)(3h -4)4. 6r² + 7r -10= (r+2)(6r -5)5. 5a² -7ab -6b²= (a -2b)(5a+3b)6. 8x² -10xy - 25y²= (4x+5y)(2x -5y)7.14m² +19mn - 3n²= (7m -n)(2m+3n)8. 18w² - z - 5z²= 9. 16h² +8hk -15k²= (4h+3k)(4h -5k)10. 10x² - 25x -60= (2x+3)(5x -20)11. 16p² -4pq - 30q²= (2p -3q)(8p+10q)12. 42r² -3rt - 9t²= (2r -t)(21r+9t)13. 6c³ + 11c² -10c= (2c+5)(3c² -2c)14. 4y² -13y -12= (y -4)(4y+3)15. 2d² +d -21= (d -3)(2d+7)16. 8m² -34m -9= (4m+1)(2m -9)17. 12f² +35f +8= (4f+1)(3f+8)

[stockpotato]

Are you asking how to apply the quadratic equation? Google quadratic equation and check wikipedia.It has the form aV^2 + bV + c, where V is the variable.In equation 1., a=6b=-1c=-2in equation 6,solving for x in terms of y,a=8b=-10yc=-25y^2The solution is always the same. You just have to know what a, b, and c are.Solution-b +/- SQRT(b^2-4ac))/2a

[dancegrl91]

1. (3x-2)(2x+1)2. (5t-2)(2t+1)3. (3h+2)(3h-4)4.(r+2)(6r-5)10.(5x-20)(2x+3)14. (4y+3)(y-4)15. (2d+7)(d-3)16. (4m+1)(2m-9)17. (4f+1)(3f+8)Good luck!

[MartyrComplex]

I'll show you one and explain how to do it..We can just do number one for instance.Okay. well, first of all you need to be familiar with the foil method.Which means thatx+y)(x+y) = (x²+xy+xy+y) OR (x²+2xy+y)This is done by multiplying out EVERY TERM.I'll show you this way. (1x+1y)(2x+2y)(the numbers are there to differentiate.)You would do the foil by multiplying 1x*2x then multiplying 1x*2y then 1y*2x then 1y*2y <<<<The Foil Method.Then you collect like terms. Okay, now that you understand the foil method.. What you're doing in these problems is breaking these trinomials down into two binomials, or the reverse of the foil method.Okay! Let's do number one.(6x²-x-2)Alright. so you know you're going to have a setup in two binomials. But what to put where?!Well, since you have a number as your lead coefficient. (the six) You might have to work more to actually factor this one.Because you have two different sets of factors for six that could be used, that's 1&6 and 2&3.So, lets just say we're going to use two and three.(2x + )(3x+ ) 2x*3x=6x (the first term of your trinomial.Now lets see.. we're looking for two back numbers.Since two is your constant, you're going to be looking for multiples of two which are only two and one. Also since you have a negative ending number, your ending numbers in your binomials have to be opposites, since two opposites make a negative! Let's try it out.(2x+1)(3x-2) Now.. foil it out to see if it's right.2x*3x=6x That's right. 2x*-2= -4x 1*3x=3x When you add like terms you get -x Which is also right. And of course 1*-2=-2. So.. Now you've factored it.. getting (2x+1)(3x-2)Now.. to get actual numeral answers...Set them equal to zero (2x+1)(3x-2)=0.2x+1=0 and 3x-2=0Now solve for both x's.2x+1=0 ---> 2x=1 ---> x=1/2 There's one x.3x-2=0 ---->3x=2 -----> x=2/3 There's your other x.And that's how you solve quadratic equations.Hope this helps.

[camateo93]

I'll try to explain how to work these kinds of problems:Let's do number 1: First, you need to find the factors or multiples of -2, and then 6 (aka factors of a and c ). For -2, you get -2 and 1, -1 and 2. Then you fin the multiples of 6: 3 and 2, 6 and 1, 1 and 6, and 3 and 2. Now you will plug those values into the equation as follows: (6x-2)(x +1). Then you multiply -2 and x, and 6x and 1, and add those two expressions together. So you will get -4x. in order for the factor to be correct, the two expressions should add up to bx in the equation, or -x in this case. So 6x-2x... Thats not right. lets try again: (3x-2)(2x+1). -4x+3x=-x. Yeah!!!! That is the answer to number one.2. (5t-2)(2t+1)3. (3h-4)(3h+2)

[davide405]

I'm going to choose one problem, and work it out for you in exhaustive detail.Using number 7 as the example:14m^2 + 19mn - 3n^2Look at the first coefficient and the last coefficient, they are 14 and -3 respectively. Find the product of those two numbers. It is -42. Now consider the middle coefficient, 19.To begin to factor this trinomial, we need to find two numbers whose PRODUCT is -42, and whose SUM is 19.The two numbers that fit those requirements are 21 and -2. That is: 21(-2) = -41, and also 21 + (-2) = 19.Now, we need to re-write the trinomial, splitting up the middle term using the two numbers 21 and -2.14m^2 + 21mn - 2mn - 3n^2Now we need to group the terms by pairs.(14m^2 + 21mn) + (-2mn - 3n^2)Now we need to factor out the greatest common monomial factor from both pairs. For the first pair of terms, this is 7m. For the second pair of terms, this is -n.7m(2m + 3n) - n(2m + 3n)Notice that the binomials in the parentheses are identical. That makes them a binomial common factor. We can now "undistribute" the two monomials, and group them as a separate binomial.(7m - n)(2m + 3n)Good luck with your assignment!