(x2-4x)(x2-4x-1)-20
plz solve it
I have done the below solution in detail for your understanding ,Do read and understand properly :
(x2-4x)(x2-4x-1)-20
x(x-4)(x2-4x-1)-20
x [x2*x – 4x*x -x + x2*(-4)- 4x*(- 4) -1* (-4) ] -20
x[ x3 -4x2 –x -4x2 +16x +4 ] -20
x[ x3 -8x2 +15x +4 ] -20
x4 -8x3 +15x2 +4x -20
Next step check for which value of ‘x’ the above polynomial will be its factor .If take the value of ‘x’ and substitute in the above polynomial if we get the value as 0 ,so this value will be its factor
Let be x= 1 if we substitute in the above polynomial ,you’ll get = -8 ,its not its factor
Then take x =-1 substitute in the above polynomial
(-1)4 -8(-1)3 +15(-1)2 +4(-1) -20
1 +8 +15 -4 -20
24-24
0
So x=-1 is a factor of x4 -8x3 +15x2 +4x -20
(x+1) is a factor of x4 -8x3 +15x2 +4x -20
Divide : x4 -8x3 +15x2 +4x -20 by (x+1)
x4 -8x3 +15x2 +4x -20 / (x+1)
You will get the QUOTIENT = x3 -9x2 +24x -20
Let for now the ans be
(x2-4x)(x2-4x-1)-20 = (x+1) (x3 -9x2 +24x -20) --------------(1)
The polynomial : x3 -9x2 +24x -20
As we did early do the same thing for which value of ‘x’ the above polynomial will be its factor.
Take x=1 you get value = -54 ,So its not its factor
Similarly take x= -1 you get value = -4 ,Again its not its factor
Then check if x=2 is the factor of polynomial x3 -9x2 +24x -20
x3 -9x2 +24x -20
(2)3 -9(2)2 +24(2) -20
8 – 36 + 48 -20
28-28
0
So x=2 is the factor of x3 -9x2 +24x -20
(x-2) is factor of x3 -9x2 +24x -20
As we did earlier
Divide : x3 -9x2 +24x -20 by (x-2)
x3 -9x2 +24x -20 / (x-2)
You will get the QUOTIENT = x2 -7x +10
We can take (1) as
(x2-4x)(x2-4x-1)-20 = (x+1) (x3 -9x2 +24x -20)
= (x+1) { (x-2) (x2 -7x +10) } -------------(2)
Check Again whether “(x2 -7x +10)” can be splitted into more factor that’s why I have taken (2)
Then,
x2 -7x +10 (10 = -2 *-5 and -2 -5 = -7)
x2 -2x-5x +10
x(x-2) -5(x-2)
(x-2) (x-5)
The Factors of “x2 -7x +10 “ = (x-2)(x-5)
In (2)
(x2-4x)(x2-4x-1)-20 = (x+1) { (x-2) (x2 -7x +10) }
(x2-4x)(x2-4x-1)-20 = (x+1) (x-2) (x-2) (x-5)
(x2-4x)(x2-4x-1)-20 = (x+1) (x-2)2 (x-5)
The Answer : (x2-4x)(x2-4x-1)-20 = (x+1) (x-2)2 (x-5)
If you are satisfied do give thumbs up .Do not give suggestion like thanxx.I am saying this because when i give the solution to other ,but when they are satisfied with my solution they do not give thumb up but they just give sugestions like thanxx .So if you are satisfied with my solution do give me thumbs up .