Tamara J. answered • 12/05/12
Math Tutoring - Algebra and Calculus (all levels)
-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)
Tamara J.
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
12/05/12
Zee B.
thank you soo much for helping me :) now i am gonna see if it works with equations like 4x^2 -27x + 4512/05/12