Please I need MATH HELP!!!!?

Question

Factoring by Grouping- Math?
If anyone could help me with these i think that they are confusing and if yuo could show me the steps of how to get to the answer that would help me so much. thanks in advanced.

Factor Completely

1. m^2 - 10m + 9
2. x^2 + 8x -20
3. 3x^2 + 10x + 3
4. 2xy - 12xz + 3y - 18z

Thanks Again!! :-)
fyi that ^ 2means squared

Answer 1

Hi !! Hope this helps !!!

answers


( 1 ) m^2 - 10m + 9

( m - 9 )( m - 1 )
When we do factorization we do the" prime factor of the terms > That was it's called the prime fractorization or just factorization .
Lets keep in mind the method of F.O.I.L. which stands for : Mult. the first term by the first term , mult. the outside term by the outside term , mult. the inside term by the inside term and mult. the last term by the last term

The first step in doing factorization for an equation such as the first example
( see below )


m^2 -10m + 9
we set up the form as below

( )( )

The first term to factor is the : m^2 : ( m ) ( m )
therefore :
( m )( m )

now te next term is : - 10m However we must pause here and do a little side work

To get the middle term we have to think of two factors that when mult. will equal 9 and when the same two terms are combined will equal -10m

we do this by trail and error " we think of all the factors of 9 that when combined will = - 10. Let try ( - 9 ) and ( - 1 ) . mult . these two terms : ( - 9 ) x ( - 1 ) = + 9 ( don't forget the " signs " )
let combined these two terms : ( - 9 ) + ( - 1 ) = - 10
there fore the form shuld look like as below :

( m - 9)( m - 1 )

and we are done This is the basic for alll factorizations .


Let check our answer

F. O. I . L.

F = frst terms by first terms : ( m ) ( m ) = m^2

0 = out. terms by out. term : ( -1 )( m ) = - 1m

I =inside terms by inside terms : ( - 9 )( m ) = - 9m

l = last terms by last terms : ( - 9 ) ( - 1 ) = + 9

now comb. the middle terms : ( - 1m ) + ( -9m ) = -10m

now on to the rest of the equations ;

2) x^2 + 8x - 20

= ( x + 10 )( x - 2 )


3) 3x^2 + 10x + 3
I could not determined a solution for this one there are no terms of 3 that when comb. that will equal 10 therefore

No solutions



4) 2xy - 12x + 3y - 18 z
this equation requires a special kind of factoring It is called factorindg by grouping In factoring by grouping we actually do group the terms together as below :

2xy - 12xz + 3y - 18 z



we group them as below

( 2xy - 12xz ) ( + 3y - 16z )

now we take each group and find a common fact in each

a) ( 2xy - 12xz )
= 2x ( y - 6z)
nw the second group

b) ( 3y - 6z )
= 3(y - 6z) now we find the common factor in both groups

( 2x + 3 )( y - 6z )


hope this helps

Answer 2

m² - 10m + 9 = m² - 9m - m + 9 = m(m-9) - (m-9) = (m-1)(m-9)

x² + 8x - 20 = x² + 10x - 2x - 20 = x(x+10) - 2(x+10) = (x-2)(x+10)

3x² + 10x + 3 = 3x(x + 3) + (x + 3) = (3x + 1)(x+3)

2xy - 12xz + 3y - 18z = 2x(y - 6z) + 3(y - 6z) = (2x+3)(y-6z)

Answer 3

m^2 - 10m + 9...m^2 and 9 are both squares
now you have to factorize -10 so that you can get 9 by adding the factors, in this case its -1 and -9, so -9+-1= -10
so now you have m^2 -9m -1m + 9
now you take out the common number/letter/combination from this
m(m-9) - 1(m-9) = (m-1)(m-9)
so your answer is m = 1 or m = 9
you can solve the rest by using this same method

Answer 4

1.(m-9)(m-1) in the original problem the signs are -/+ so it factors to -/- find factor of 9 that add up to 10
2.(x+10)(x-2)signs are +/- so factors to +/- find factors of -20 add to 8
3.(3x+1)(x+3)+/+ so factors to +/+ 3 only factors to 3&1 find the right spot for those numbers to add up to 10
4.(2x-3)(y-6z) reverse FOIL to get 2xy u need to (2x-?)(y-?) to get 12 xz (2x-?)(y-6z) and to get 3y (2x-3)(y-6z) & 6z x 3 =18z always double check answers

Answer 5

1. (m-1)(m-9)
2. (x+10)(x-2)
3. (3x+1)(x+3)
4. y(2x+3) - z(12x+18) = y(2x+3) - 6z(2x+3) = (2x+3)(y-6z)

Answer 6

m^2-m-9m+9=m(m-1)-9(m-1)=(m-1)(m-9)
x^2+10x-2x-20=x(x+10)-2(x+10)=(x+10)(x-2)
3x^2+9x+x+3=3x(x+3)+(x+3)=(x+3)(3x+1)
2x(y-6z)+3(y-6z)=(y-6z)(2x+3)