Factorising?! (Algebra)?

[SophieBee]

I got an equation for homework which is 6 bsquared - 11b + 4 = (3b-4) x (____). Could anybody help me with filling in the gap, and also explain it to me?

[Navek6414]

6b^2 - 11b + 4 = 0(3b-4) x (____)first they gave u a 3b... what multiplies with 3b to get 6b^2?as seen in [6b^2] - 11b + 4 = 02b..so now you have (3b-4) x (2b__)now they gave you -4, what multiplies with -4 to get +4 as seen in6b^2 - 11b [+ 4] = 0-1so(3b-4) x (2b-1)multiply it out and make sure it equals to original equation6b^2 - 3b - 8b + 4and surely enough you get same answer

[kindricko5857]

6b^2 - 11b + 4ac = 6(4) = 24Factors of 24 that add to - 11 are -8 & -36b^2 - 8b - 3b + 4 {rewrite for grouping}2b(3b - 4) - 1(3b - 4)(2b - 1)(3b - 4)

[confused8698]

divide (6b^2-11b+4) by (3b-4). the quotient will fill the gap..which is (2b-1).

[theripper9876]

ok the equation is in ax + bx + c form...6b^2 - 11b + 4in order to figure this out you must multiply a*c6*4 = 24you must find what multiplies to a*c and adds to bso what multiplies to 24 and adds to -11these numbers are -8 and - 3-8*-3 = 24 and -8+-3 = -11so seperate your equation like this6b^2 - 8b - 3b + 4now factor this by grouping (factoring out what is common from the first two terms, then the second two)2b( 3b - 4) - 1 (3b - 4)now pull apart, THESE ARE YOUR ANSWERS(2b - 1) (3b - 4)you can also check by using the FOIL method (first ouside inside last)2b * 3b = 6b^22b * -4 = - 8b3b * -1 = - 3b-1 * -4 = 4so 6b^2 - 11b + 4, so the solutions above work

[RohitC]

*=multiplication signWe write bsquared as b^26 b^2 - 11b + 4 = (3b-4) x (____)Let the missing term =ALets factorise 6 b^2 - 11b + 46 b^2 - 11b + 4 = (3b-4)*(2b-1)6 b^2 - 11b + 4 = (3b-4) xA (3b-4)*(2b-1)=(3b-4)*AA=(3b-4)*(2b-1)/(3b-4)Missing term=A=2b-1To factorise 6 b^2 - 11b + 4, we can use discriminantFor a general equation ax^2+bx+c=0,Discriminant=b^2-4*a*cDiscriminant=D=(-11)^2-4*6*4D=121-96=25sqrt(D)=sqrt(25)=5Formula for x in equation ax^2+bx+c=0 isx= (-b+sqrt(D))/2a and x= (-b-sqrt(D))/2aSo, in the equation 6 b^2 - 11b + 4=0b=(11+5)/12=16/12 and b=(11-5)/12=6/12b=4/3 and b=1/2So, taking b=4/3 and taking b=1/2 3b=4 2b=1 3b-4=0 2b-1=0So, equation 6 b^2 - 11b + 4=0 means (3b-4)*(2b-1)=0

[shadowca1964]

question: 6b^2-11b+4 and giving the first factor is (3b-4)(3b-4)( )now what times 3b will give you 6b^2?answer 2b(3b-4)(2b+/- x)3b times what x minus 8b will give you -11b3bx-8b= -11b3bx = -3bx=-1final answer (3b-4)(2b-1)

[Javier5310]

6b^2 - 11b + 4 = ( 3b - 4 ) * ( ___ )First you have to find what expression multiplied by 3b-4 will give you 6b^2 - 11b + 4. For that you can use this method:When you multiply 2 expressions like this (ax+b)*(cx+d) you get:.......(ac) x^2 + (ad+bc) x + (bd)If you have the last expression you can find the factors just like this:.acx^2 + (ad+bc)x + bd ........ax..................+b........cx.......... ........+d...ax*d+cx*b= (ad+bc)xYou multiply the numbers you found below to see if you get the expression from the middle (ad+bc). If you got it then you choose correctly the factors, if you don't then you should keep trying. Let's solve the exercise:You already know one of the factors is 3b-4 so you just copy it and then find the other one:......6b^2 - 11b + 4-->..3b...............-4......2b...............-1Now let's multiply to see if we get the expression from the middle:.....3b*(-1)+2b*(-4) = -3b-8b = -11bIt's the same so it's the correct answer.You could have chosen also this factors:.....6b^2 - 11b + 4.....6b...............-4.....1b...............-1But if you multiply 6b*(-1)+ 1b*(-4) = -14b.It's not correct cause you don't get the expression from the middle.