+0  
 
0
51
12
avatar+194 

We were given factoring questions and no one ive contacted has any clue how to do them so to the internet i go!

 

1) 3a^2-10a-8

 

and

2) 30x^2-9x-3

 

and

3) 16-25x

 

also

4) 4(2-a)^2 -81

 

thanks in advance :)

Baneofwizard  Nov 21, 2018
 #1
avatar+14579 
+2

Example

1   (3a +2)(a-4)            the  numbers   2   and -4   must multiply to equal  '-8'  

2    (15x+3)( 2x-1)        again.....the   3  and  -1    multiply to -3   and the 15 and 2 multiply to 30

3     This one is factored as far as it can be

4    4 (a^2 -4a +4) - 81

       4a^2-16a+16 - 81

       4 a^2-16a-65          

ElectricPavlov  Nov 21, 2018
 #4
avatar+456 
+1

You can simplify \(4a^2-16a-65\)

CoolStuffYT  Nov 21, 2018
 #5
avatar+14579 
+1

If you use the quadratic formula you will find   a= 52/8   or -20/8

    then you would have      (a-52/8)(a+20/8)        but you will see that   a x a = a^2   NOT 4 a^2.....

        so lets multiply both terms by 2

                  (2a-52/8 * 2)( 2a+20/8 *2)

                   (2a-13)(2a+5)    

ElectricPavlov  Nov 21, 2018
 #2
avatar
0

4)

 

 Factor the following:
4 (2 - a)^2 - 81

4 (2 - a)^2 - 81 = (2 (2 - a))^2 - 9^2:
(2 (2 - a))^2 - 9^2

Factor the difference of two squares. (2 (2 - a))^2 - 9^2 = (2 (2 - a) - 9) (2 (2 - a) + 9):
(2 (2 - a) - 9) (2 (2 - a) + 9)

2 (2 - a) = 4 - 2 a:
(2 (2 - a) - 9) (4 - 2 a + 9)

Grouping like terms, -2 a + 4 + 9 = (4 + 9) - 2 a:
(4 + 9) - 2 a (2 (2 - a) - 9)

4 + 9 = 13:
(2 (2 - a) - 9) (13 - 2 a)

2 (2 - a) = 4 - 2 a:
(4 - 2 a - 9) (13 - 2 a)

Grouping like terms, -2 a - 9 + 4 = -2 a + (4 - 9):
-2 a + (4 - 9) (13 - 2 a)

4 - 9 = -5:
(-5 - 2 a) (13 - 2 a)

Factor -1 out of -2 a - 5:

-(2a + 5) (13 - 2a)

Guest Nov 21, 2018
 #3
avatar+456 
+1

1) Factor out (a      )(3a      )

See the multiples of -8 and have them add up to -10 when one of them is multiplied by 3.

You get \((a-4)(3a+2)\)

 

2) The multiples of -3 are 1, -3 and -1, 3 and after trying out we get \((15x^2+3)(2x-1)\)

 

3) We see that we can do a difference of squares. \((4+5\sqrt x)(4-5\sqrt x)\) .

 

4) This equals \(4(a^2-4a+4)-81=4a^2-16a+16-81=4a^2-16a-65\)

Factor \(4a^2-16a-65=(2a+5)(2a-13)\) .

 

You are very welcome!

:P

 

(also thanks PartialMathematician for pointing out a mistake!)

CoolStuffYT  Nov 21, 2018
edited by CoolStuffYT  Nov 21, 2018
 #9
avatar+784 
+3

#3 could be factored into \(4^2 - 5^2(x)\)

PartialMathematician  Nov 21, 2018
 #10
avatar+784 
+4

We could also substitute \(y^2\) for \(x\), so we have \(16-25y^2\). Now, this looks looks like a difference of squares. We can factor it into \((4+5y)\cdot(4-5y)\). Substituting back \(x\) for \(y^2\), we have \(\boxed{(4+5\sqrt{x})\cdot(4-5\sqrt{x})}\)

 

Hope this helps,

- PartialMathematician

PartialMathematician  Nov 21, 2018
 #12
avatar+456 
0

You are right, thanks.

CoolStuffYT  Nov 21, 2018
 #6
avatar+92856 
+1

We can actually factor 3 as a difference of squares  if we note that

 

x  = √x * √x

 

16 - 25 x   =

 

(4 + 5√x ) ( 4 - 5√x )

 

 

cool cool cool

CPhill  Nov 21, 2018
 #7
avatar+92856 
+1

Also

 

4) 4(2-a)^2 -81     is a difference of squares

 

[ 2 (2-a) + 9 ]  [ 2(2-a) - 9 ]   =

 

[4 - 2a + 9 ]  [ 4 - 2a - 9 ]    =

 

[13 - 2a ] [ -5 - 2a ] =       { factor a "-1" from the last term....move it to the front }

 

- [13 - 2a ] [ 5 + 2a ]

 

[ 2a - 13 ] [ 2a + 5 ]

 

 

 

cool cool cool

CPhill  Nov 21, 2018
 #8
avatar+14579 
+1

Wooohoooo!  Nice, Chris !

ElectricPavlov  Nov 21, 2018
 #11
avatar+92856 
0

Thanks, EP.....sometimes....my brain actually works!!!

 

 

cool cool cool

CPhill  Nov 21, 2018

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