Help with factoring a problem?

Question

I have trouble with factoring too, and this problem is the hardest for me.

----Factor completely with respect to the integers

(2x^3)-(3x^2)+(4x)-(6)

To make it easier to see, I've added ( ) around the variables, but they are NOT in the original problem.

Thanks for any help, I really need it.

Answer 1

Regroup it,

[(2x^3)-(3x^2)] + [(4x)-(6)]

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

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

Answer 2

ok for this u use factor by grouping

(2x^3)-(3x^2)+(4x)-(6)

factor the first 2 terms then the last 2

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

byt he assosciative property

we can pull out a factor

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

and thats the answer

Answer 3

Hi,

Factor by grouping first two terms and last two terms, looking for a GCF from each pair.

2x³ - 3x² + 4x - 6 =

x²(2x - 3) + 2(2x - 3) =

(x² + 2)(2x - 3) <==ANSWER

I hope that helps!! :-)

Answer 4

This cubic function or algebraic polynomial is quite intricate to factor but as soon as you carefully scrutinize the equation, you can see a pattern in the integral factors with respect to their powers.  For the cubic equation y = 2x^3 - 3x^2 + 4x - 6, you have to observe the two coefficients with the last two and see a common relationship in their multiples or divisors.  By factoring out -x^2 for the first two coefficients, you have -x^2(3 - 2x), which then implies the associative && distributive property. The goal of this cubic equation is to make the factors identical to write a factor of two that would involve a quadratic and linear factor such as the following: -2(3 - 2x).  All together, the factorization of the cubic equation is: y = x^2(2x - 3) + 2(2x - 3).  Thus, the factorization of the cubic algebraic function of y = 2x^3 - 3x^2 + 4x - 6 is y = (x^2 + 2)(2x - 3).  By solving the equation, you have the following solutions: x = 3/2.

J.C