SOLUTION: Factor completely 1)x^3-6x^2+11x-6 given that x-1 is a factor 2)x^2+6x+9=0 3)2x^2+5x-12=0 4)3x^3=12x 5)(2x-1)(3x+5)=5

Question 149109: Factor completely
1)x^3-6x^2+11x-6 given that x-1 is a factor

2)x^2+6x+9=0

3)2x^2+5x-12=0
4)3x^3=12x
5)(2x-1)(3x+5)=5

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
1)
(x^3-6x^2+11x-6)/(x-1) Long division or synthetic division.
=x^2-5x+6
=(x-3)(x-2)
.
2)
x^2+6x+9=0
(x+3)^2=0
x=-3
.
3)
2x^2+5x-12=0
2*-12=-24... 8 and -3 are factors of -24 that when added equal 5.
2x^2+8x-3x-12=0
2x(x+4)-3(x+4)=0
(2x-3)(x+4)=0
2x=3
x=3/2
x=-4
.
4)
3x^3=12x
3x^3-12x=0
3x(x^2-4)=0
3x(x+2)(x-2)=0
x=0, x=-2, x=2
.
5)
(2x-1)(3x+5)=5
6x^2+7x-5=5
6x^2+7x-10=0
6*-10=-60... 12 and -5 are factors of -60 whose sum is 7.
6x^2+12x-5x-10=0
6x(x+2)-5(x+2)=0
(6x-5)(x+2)=0
6x=5
x=5/6
x=-2
.
Ed

RELATED QUESTIONS
Factor completely, 11x(4x-3)-6(4x-3)= 2x(x-5)-(x-5) 3x^3-4x^2+6x-8=... (answered by KMST)

Factor completely: x^3 � 2x^2 + 6x � 12 . Factor completely: x^2 + 17x + 16... (answered by stanbon,edjones)

Completely factor the polynomial 3x*3+12x*2+3x+12 Factor the trinomial completely... (answered by lynnlo,Alan3354)

Expand and simlify (a) -3(x� - xy + 2y�) -3x�+3xy-6y� (b) (x � 1)(x + 4)... (answered by geE-thug)

Find the area of a room that has a width of (x+3) and a length of (2x-5). (2.0 points)... (answered by nyc_function)

1. 2x^2+10x+12 Factor completely 2.x^2+8x=-16 3.x^2-16=0 4. x^2-16x=-64 5. (answered by ankor@dixie-net.com)

1- {{{5a^2-6a+1=0}}} 2- {{{2x-x^2=-24}}} 3- x^+3x=0 4- {{{6x(x-12)=0}}} 5-... (answered by khv_maths)

can you solve these problems in steps? Set2 1. solve the equation 5x+3=-15, for x... (answered by rapaljer)

1.Graph y=| x - 2 | +3 2.Graph y<2x-2 y>1/2x-2 3. Find a32 for arithmetic... (answered by Alan3354)