I need help factoring polynomials. Can someone help me factor 4x^2+81-36x. I need to show work too. Thank you
2006-09-12 14:35:05 · 7 answers · asked by QDPie 2 in Education & Reference ➔ Homework Help
^2 means exponent or to the 2nd power
2006-09-12 14:47:42 · update #1
the equation 4x^2+81-36x=0 has double zeros at x=4.5. therefore:
4x^2+81-36x=4(x-4.5)^2
2006-09-12 14:44:50 · answer #1 · answered by Amir D 2 · 0⤊ 0⤋
First you need to write it out in a standard form:
4x^2-36x+81
Since it is a Quadratic equation it will factor into two terms similar to (Ax + B)(Cx + D)
You know that A*C = 4 because Ax*Cx = 4x^2...
so you will have something like (4x + B)(x +D)...
.........................or... (2x +B)(2x+D)
You also know that B*D = 81 BUT...
because the middle term in NEGATIVE, B and D must be negative!!! (9*9), (3*27), (27*3), (1*81), (81*1)
You also know that AD + BC = -36 (since 36 = 4*9 this makes 2*9 look tempting for each one)... so let's try it...
(2x-9)(2x-9) = 4x^2 -18x -18x +81 = 4x^2 -36x +81 CHECK!
2006-09-12 21:52:41 · answer #2 · answered by ♥Tom♥ 6 · 0⤊ 0⤋
You can use the completing the square method.
Move the constant terms to one side:
4x^2-36x= -81
now divide by 4 to get the x^2 set to 1
x^2 - 9x = -20.25
now you need to find the number that you can add to the left side to make it a pefect square. you do this by calculating (b/2)^2. In this case b = -9 so you need to add 81/4 to each side
x^2 -9x +(81/4) = 0
now by definition of the square you can collapse the left side into the form (x - b/2)^2 or in this case (x-9/2)^2
Note: ^2 = "raised to the power of 2"
So when I write (x- 9/2)^2 it really is the same as writing:
(x - 9/2 ) * (x - 9/2)
2006-09-12 21:46:24 · answer #3 · answered by mdigitale 7 · 0⤊ 0⤋
I 'll give U simple trick.
rearrange the polynomial
4x^2 -36x +81
a) take sq.root of first term i.e 2x
b) sq.root of last term i.e .9
C) place the middleterm sign.
Here is ur ans ...... ( 2x -9 )^ 2
or (2x -9) (2x-9 )
2006-09-13 14:48:21 · answer #4 · answered by macline k 2 · 0⤊ 0⤋
Rearrange the expression to 4x^2-36x+81.
(2x-9)*(2x-9)
There's not much work to show...
2006-09-12 21:41:04 · answer #5 · answered by stratocaster81 2 · 0⤊ 0⤋
4x^2+81-36x
wats with the ^....fix this q and i will help u out.....i'l check bk in a seond to see if u fixed it....if u haven't i won't help u
2006-09-12 21:38:25 · answer #6 · answered by matrix15sam 3 · 0⤊ 0⤋
4x^2 -36x +81
4x^2- 18x-18x+81
2x(2x-9) -9(2x-9)
(2x-9)(2x-9)
(2x-9)^2
2006-09-13 07:34:03 · answer #7 · answered by mj 2 · 0⤊ 0⤋