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Can u please help me to factor completely

I am only in the comfort of the box method, and i still dont know how to factor or even know what is the common factor. I am given questions like x^2 - 144 and p^2 + 64 + 16p. The biggest problem i have with this is the question -7x^2 + 2x^3 + 4x - 14

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1 Answer

     -7x2 + 2x3 + 4x - 14

First, rearrange the equation into descending order of powers:

     2x3 - 7x2 + 4x - 14

Look at the first two terms and the last two terms separately to see if there is a greatest common factor you can factor out:

      2x3 - 7x2        ==>   notice that you can factor out an x2 from both terms

                             ==>   2x3 - 7x2  =  x2·(2x - 7)

      4x - 14           ==>   notice that you can factor out a 2 from both terms

                             ==>   4x - 14  =  2·(2x - 7)

Now you have arrived at the following:

      2x3 - 7x2 + 4x - 14     ==>     x2·(2x - 7) + 2·(2x - 7)

Notice that there is a greatest common factor among the two terms from the new equation we found, that being  2x - 7. So we factor this out of both terms:

      x2·(2x - 7) + 2·(2x - 7)     ==>     (2x - 7)·(x2 + 2)

Thus,

          2x3 - 7x2 + 4x - 14   =   (x2 + 2)(2x - 7)

Comments

thank you soo much for helping me :) now i am gonna see if it works with equations like 4x^2 -27x + 45

Well this method won't work on that kind of problem b/c it's a 2nd degree polynomial, whereas the one solved above is a 3rd degree polynomial.

To factor 4x2 - 27x + 45, we first want to find common factors of the first and last coefficients:

   Factors of 4:      ±1*±4, ±2*±2

   Factors of 45:    ±1*±45, ±3*±15, ±5*±9

We need to choose a pair whose products will add up to be the middle coefficient, -27. That turns out to be +1*+4 and -3*-15,                                  since 1*-15 + 4*-3 = -15 + -12 = -15 - 12 = -27

     4x2 - 27x + 45 = (x - 3)(4x - 15) 

                           = x·4x + x·-15 - 3·4x - 3·-15

                          = 4x2 - 15x - 12x + 45

                          = 4x2 - 27x + 45

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