Help With Algebra H. Please!?

Question

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2 questions.

How do you factor this expression?

3x^2 - 5x - 2

or

6x^3 - 15x^2 - 9x



And how would you solve this?

x^2 - 2x - 15 = 0

Answer 1

3x^2 - 5x - 2
(3x + 1)(x - 2)


6x^3 - 15x^2 - 9x
3x(2x^2 - 5x - 3)
3x(2x + 1)(x - 3)


x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x - 5 = 0 AND x + 3 = 0
x = 5 AND x = -3

Answer 2

Factor
3x² - 5x - 2

(3x + 1)(x - 2)


6x^3 - 15x^2 - 9x

3x(2x^2 - 5x - 3)

3x(2x + 1)(x - 3)

Solve

x² - 2x - 15 = 0

(x - 5)(x + 3) = 0

x = 5, x = -3
.

Answer 3

3x^2 - 5x - 2
= (3x + 1)(x - 2)

6x^3 - 15x^2 - 9x
= 6x^2 - 15x - 9
= (3x + 9)(2x - 1)x

x^2 - 2x - 15 = 0
= (x - 5)(x + 3)
x = 5, x = -3

Answer 4

3x^2 - 5x - 2
= 3x^2 - 6x + x - 2
= 3x(x-2)+1(x-2)
= (x-2)(3x+1)

6x^3 - 15x^2 - 9x
= 3x(2x^2 - 5x - 3)
= 3x(2x^2 -6x+x-3)
= 3x(2x(x-3)+1(x-3))
= 3x(x-3)(2x+1)

x^2 - 2x - 15 = 0
x^2 - 5x + 3x - 15 = 0
x(x-5)+3(x-5)=0
(x-5)(x+3)=0
x-5=0 --- x=5
x+3=0 --- x=-3
x={-3,5}

Answer 5

To factor the given expression you must first find its roots, i.e. the values of X where the expression becomes 0. For the first expression the answer is X1=-1/3 and X2=2. Next, given its roots X1 and X2, you can always express the given (or any equation of the form aX^2+bx+c) expression through a(X-X1)(X-X2), where a stands for the coefficient by X^2 => 3x^2 - 5x - 2=3(x-2)(x+1/3).
To solve, you must find d=SQRT(b^2-4ac), and then X1=(-b+d)/2a and X2==(-b-d)/2a (a, b, and c stand for respective coefficients in the above expression).

Answer 6

number 1:

3x^2-5x-2=

(3x+1)(x -2)
~~~~~~~~~~

number 2

6x^3-15x^2-9x

GCF:x(you could take it out)

3x(2x^2-5x-3)

3x(2x+1)(x-3 )
~~~~~~~~~~~

number 3

just factor it

(x+3)(x-5)=0

so you get x+3=0, and x-5=0

solve these
----------------

x+3=0

x=-3
------------

x-5=0

x=5
-----------

so final answer for #3 is x= -3 and 5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(remember when ever its equal to zero, you get 2 answers) =)

Answer 7

3X^2-3X-2X-2=0
3X(X-1) -2(X-1)=0
(3X-2)(X-1)=0



X^2-2X-15=0
X^2-5X+3X-15
X(X-5)+3(X-5)
(X+3)(X-5)