Question

Factor the trinomial 4x2 + 24x + 11

once i get it broken down to 4x^2+22x+2x+11 i am stuck, what is the next step?

Answer 1

4x^2+24x+11

Answer 2

(2x+11)(2x +1)

Answer 3

can you show me how you got that?

Answer 4

well its trial and error
first assume its 2x and 2x in the firstbpart of the bracket
now u nedd to numbers which when multiplied together give 11, and when multiplied by 2 and added give 24

these numbers are 1 and 11

OUtside numbers give 2x * 11 = 22x
and inside give 2x * 1 = 2x

2x + 22x = 24x

Answer 5

i was just confused becaquse my book told me to multiple 4x and 11 as the first step so i got 44x which would be x+22 and x+2 cus they add to 24 and mulitply to 44 but then once i split the middle term im stuck

Answer 6

Ok lets try factoring

x^2 - x - 6

first part of brackets will be x (to give x^2

(x )(x )

Now we need 2 numbers which when multip;ies will give -6 and when added will give -1.

these 2 numbers are -3 and 2:-
-3 * +2 = --6
and -3 + 2 = -1

so our answer is

(x -3)(x + 2)

Answer 7

right i understand that i just dpnt get what to do when that x has a leading coeeficiant like
4x^2+24x+11

Answer 8

yeah there are a few ways do do this - I personally prefer the way ive shown

Answer 9

which was the trial and error method?

Answer 10

step1; factor out commons; nothing factors move to step 2

step2; setup as if it factors:

(x ) (x )

step3; multiply the first and last numbers to get a pool of options; and divide out the first from the set up:

(x /4) (x /4)

4(11) = 44

step4; observe the signs of the middle and last numbers to fill in the setup;

+24; +11. the last number tells us to add; the middle number says the bigger number is +; which would make better sense in another problem, but lets go with it :)

(x+B/4) (x+ S/4)

step5; go thru the factors to determine the numbers to fill in:

1,44; 1+44 = 45 .... toss it
2,22; 2+22 = 24 .... yay!! we can use it

step6 ; fill in the setup

(x+ 22/4) (x+ 2/4)

step7; reduce till you cant reduce no more

(x+ 11/2) (x+1/2)

step8; if theres still a fraction; throw the bottom in front

(2x +11) (2x +1)

step9 ; dont forget to include the factor from step 1; in this case, there is none

Answer 11

i kind of see it there, im going to try the next problem

Answer 12

Factor the trinomial 9x2 - 18xy + 5y2

Answer 13

the one i've demonstrated above.

u can write them in columns if u like


4x^2 11 24

2 X 2 11 X 1 2X11 + 2 X 1 = 24

Answer 14

my setup is: (x y/9)(x y/9)

the last sign says + and the middle says - is bigger

(x- By/9)(x- Sy/9)

9(5) = 45

1,45; 3,15 ... 3+15 - 18

(x -15y/9)(x -3y/9)

(x -5y/3)(x -y/3)

(3x -5y) (3x -y)

Answer 15

your dividing them?

Answer 16

my way; you multiply the first into the last; so in the end you have to divide it out again

Answer 17

oh my i am so confused lol

Answer 18

9 +5 -18

3 X 3 -5 X -1 3 X -5 + 3 X -1 = -18


so the factors are (3x -5y)(3x - y)

Answer 19

when there is no leading coeff; or rather, it is 1; then you simply address the last number to get your options

Answer 20

i See it !!!
thank you

Answer 21

this way; you use it to make life easier to begin with; and remember to take it back out when your finished

Answer 22

i like how its broken down into columns that makes it a lot easier to see

Answer 23

thats quite a good way amis - logical

Answer 24

whatever u find easiest - thres really no 'right way'

Answer 25

yep; but there are plenty of wrong ways lol

Answer 26

yea