SOLUTION: Given f(x)=x^3+6x^2+11x+6 Show that f(-2)=0 and find the three factors of f(x)

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Question 366515: Given f(x)=x^3+6x^2+11x+6 Show that f(-2)=0 and find the three factors of f(x)
Found 2 solutions by CharlesG2, ewatrrr:
Answer by CharlesG2(834)   (Show Source): You can put this solution on YOUR website!
Given f(x)=x^3+6x^2+11x+6 Show that f(-2)=0 and find the three factors of f(x)


f(x)=x^3+6x^2+11x+6
f(-2) = (-2)^3 + 6(-2)^2 + 11(-2) + 6
f(-2) = -8 + 6 * 4 - 22 + 6
f(-2) = -8 + 24 - 22 + 6
f(-2) = 16 - 22 + 6
f(-2) = -6 + 6
f(-2) = 0, so x = -2 is a root when f(x) = 0, so that means x + 2 is a factor
..........x^2 + 4x + 3
x + 2 --> x^3 + 6x^2 + 11x + 6
..........x^3 + 2x^2
................4x^2 + 11x
................4x^2 + 8x
........................3x + 6
........................3x + 6

x^2 + 4x + 3
(x + 1)(x + 3) --> test with FOIL, First Outer Inner Last
x^2 + 3x + x + 3
x^2 + 4x + 3, yes

the factors are x + 2, x + 1, x + 3
the roots are -2, -1, -3


Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi, 

f(x)=x^3+6x^2+11x+6 

x = -2 is one zero

By division, we find:



       x^2  + 4x  + 3

     __________________________

x+2 | x^3 +  6x^2 + 11x  + 6 



 x^2  + 4x  + 3 

(x + 3)(x + 1)

three factors are:

(x+2)(x+3)(x+1) 

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