2006-08-08 21:16:53 · 14 answers · asked by stephanie 1 in Science & Mathematics ➔ Mathematics
(2x-3)^2 x (2x-3)(x+1)+(x-3)
(2x-3)^2 X (2x^2 -x -3 + x - 3)
(2x-3)^2 X (2x^2 - 6) (take out the 2)
Equals:
2 X (2x-3)^2 X (x^2-3) or 2 (2x-3)^2 (x^2-3)
:-)
2006-08-14 06:49:26 · answer #1 · answered by Yada Yada Yada 7 · 0⤊ 1⤋
When the equation y=(2x-3)^3 (x+1) +(x-3) (2x-3)^2 is plotted on a plotting programme such as Graphmatica, the roots are x=-1.73, x=1.5(repeated root) and x=1.73. Since 1.73 is approximately sqrt3, the expression can be factorised to give: 2(x+sqrt3)(x-sqrt3)(2x-3)^2.
The coefficient of the term with the largest power of x (x^4) must be 8, so I added the 2 in front.
2006-08-15 23:15:41 · answer #2 · answered by klwh_88 2 · 0⤊ 0⤋
Expression = (2x-3)^3 (x+1) + (x-3) (2x-3)^2
= (2x -3)^2 [ (2x-3) (x+1) + (x-3)]
= (2x-3)^2 [2x^2 - 6]
= 2 (2x-3)^2 [x - sqrt3] [x + sqrt3]
2006-08-14 04:04:34 · answer #3 · answered by baskaran r 2 · 1⤊ 0⤋
First do the first half:
(2x-3)^3 (x+1)=
(2x-3)(2x-3)=4x^2 -12x +9
Now multiply that again by (2x-3)
(4x^2 -12x +9)(2x-3)=8x^3 -36x^2 + 36x +18
Now multiply that with (x+1)
(8x^3 -36x^2 + 36x +18)(x+1)=8x^4 -28x^3 +18x^2 +27x-27
That is the answer to the first have: 8x^4 -28x^3 +18x^2 +27x-27
Now do the second half, the part after the + sign. Since you already did (2x-3)(2x-3) or (2x-3)^2 you save youself some work.
(2x-3)^2= 4x^2 -12x +9
Now multiply that with (x-3)
(4x^2 -12x +9)(x-3)=4x^3 -24x^2 +45x -27
That is the answer to the second half: 4x^3 -24x^2 +45x -27
Now add the first have and the second half together adding like terms:
(8x^4 -28x^3 +18x^2 +27x-27) + (4x^3 -24x^2 +45x -27)
=8x^4 -24x^3 -6x^2 +72x -54
That is your answer!
2006-08-16 11:55:06 · answer #4 · answered by livingall_4_god 2 · 0⤊ 0⤋
(2x - 3)^3(x + 1) + (x - 3)(2x - 3)^2
((2x - 3)^2)(((2x - 3)(x + 1)) + (x - 3))
((2x - 3)^2) ((2x^2 + 2x - 3x - 3) + x - 3)
((2x - 3)^2)(2x^2 - x - 3 + x - 3)
((2x - 3)^2)(2x^2 - 6)
2((2x - 3)^2)(x^2 - 3)
2006-08-09 04:19:05 · answer #5 · answered by Sherman81 6 · 1⤊ 0⤋
[(2x-3)^2]{[(2x-3)(x+1)]+[(x-3)]}
(2x-3)^2 (2x^2-x-3+x-3)
(2x-3)^2 (2x^2-6)
Final Answer: 2(x^2-3)(2x-3)^2
2006-08-12 23:27:36 · answer #6 · answered by fictitiousness ;-) 2 · 1⤊ 0⤋
(2x-3)^2 [(2x-3)(x+1)+(x-3)]
2006-08-16 19:33:29 · answer #7 · answered by jaredkomahalko 2 · 0⤊ 0⤋
2((2x-3)^2)(x^2 -3)
2006-08-16 15:19:09 · answer #8 · answered by nirvana 2 · 0⤊ 0⤋
2(x - 1)(2x - 3)(2x^2 - 2x - 3)
2006-08-08 21:26:24 · answer #9 · answered by JoeSchmo5819 4 · 0⤊ 1⤋
(2x-3)^3 (x+1) +(x-3) (2x-3)^2
=[(2x-3)^2]* [ (2x-3)(x+1) +(x-3) ]
=[(2x-3)^2]* [ 2x^2 -2x -3 +x-3 ]
=[(2x-3)^2]* [ x^2 -x -6 ]
=[(2x-3)^2]*(x-3)(x+2)......thats all
2006-08-08 22:11:32 · answer #10 · answered by balu 1 · 0⤊ 1⤋