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 Feb 7, 2018

Best Answer 

 #1
avatar+8579 
+3

Notice that  f(x)  factors like this...

 

f(x)   =   x3 + 4x2 - 9x - 36

                                              Factor  x2  out of the first two terms; factor  -9  out of the last two terms.

f(x)   =   x2(x + 4) - 9(x + 4)

                                              Factor  (x + 4)  out of both remaining terms.

f(x)   =   (x + 4)(x2 - 9)

                                              Factor  x2 - 9  as a difference of cubes.  x2 - 9   =   (x + 3)(x - 3)

f(x)   =   (x + 4)(x + 3)(x - 3)

 

So the factors of  f(x)  are  (x + 4) ,  (x + 3) ,  and  (x - 3) .

 Feb 8, 2018
 #1
avatar+8579 
+3
Best Answer

Notice that  f(x)  factors like this...

 

f(x)   =   x3 + 4x2 - 9x - 36

                                              Factor  x2  out of the first two terms; factor  -9  out of the last two terms.

f(x)   =   x2(x + 4) - 9(x + 4)

                                              Factor  (x + 4)  out of both remaining terms.

f(x)   =   (x + 4)(x2 - 9)

                                              Factor  x2 - 9  as a difference of cubes.  x2 - 9   =   (x + 3)(x - 3)

f(x)   =   (x + 4)(x + 3)(x - 3)

 

So the factors of  f(x)  are  (x + 4) ,  (x + 3) ,  and  (x - 3) .

hectictar Feb 8, 2018

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