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# Is the binomial a factor of the polynomial function?

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Feb 7, 2018

### Best Answer

#1
+8146
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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+0 Answers

#1
+8146
+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