SOLUTION: How do you factor second degree polynomials? Then how do you know if it's addition or subtraction? x^2-18x+45=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you factor second degree polynomials? Then how do you know if it's addition or subtraction? x^2-18x+45=      Log On


   

Question 603295: How do you factor second degree polynomials? Then how do you know if it's addition or subtraction?
x^2-18x+45=
Found 2 solutions by lynnlo, Edwin McCravy:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
x²-18x+45

Write this:

(x    )(x   )

List all the ways to factor 45, starting with 45*1  

45*1=45
15*3=45
 9*5=45

The last sign is +  (from +45), so out beside them, ADD them:

45*1=45  45+1=46
15*3=45  15+3=18
 9*5=45   9+5=14

We see that 15+3 was 18, the absolute value of the middle
coefficient, so we fill in these

(x 15)(x 3)

We do a mental FOIL ignoring signs

Since the last sign is +, both signs have the same sign, the same
sign as the middle term -18x, which is -, so the answer is

(x-15)(x-3)

-------------------------

Another example:

x²+3x-28

Write this:

(x  )(x  )

List all the ways to factor 28 starting with 28*1

28*1=28
14*2=28
 7*4=28

The last sign is -  (from -28), so out beside them, SUBTRACT them:

28*1=28  28-1=27
14*2=28  14-2=12
 7*4=28   7-4=3

We see that 7-4 was 3, the absolute value of the middle coefficient,
so we fill in these

(x 7)(x 4)

We do a mental FOIL ignoring signs

Since the last sign is -, the signs are opposite, so the LARGER,
which is 7, gets the same sign as the middle term +3x, which is +, so the answer is

(x+7)(x-4)

Edwin