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

## Can u please help me to factor completely

# 1 Answer

-7x^{2} + 2x^{3} + 4x - 14

First, rearrange the equation into descending order of powers:

2x^{3} - 7x^{2} + 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:

**2x**^{3}** - 7x**^{2} ==> notice that you can factor out an x^{2} from both terms

==> 2x^{3} - 7x^{2} = **x**^{2}**·(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:

2x^{3} - 7x^{2} + 4x - 14 ==>
**x**^{2}**·(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:

x^{2}·(2x - 7) + 2·(2x - 7) ==>
**(2x - 7)·(x**^{2}** + 2)**

Thus,

** 2x**^{3}** - 7x**^{2}** + 4x - 14 = (x**^{2}** + 2)(2x - 7)**

## Comments

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 4x

^{2}- 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

4x

^{2}- 27x + 45 = (x - 3)(4x - 15)= x·4x + x·-15 - 3·4x - 3·-15

= 4x

^{2}- 15x - 12x + 45= 4x

^{2}- 27x + 45Comment