SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x4 + 4x3 + 13x2 + 16x + 4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x4 + 4x3 + 13x2 + 16x + 4      Log On


   

Question 1001365: Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29+=+3x%5E4+%2B+4x%5E3+%2B+13x%5E2+%2B+16x+%2B+4+
f%28x%29+=+3x%5E4%2B+12x%5E2+%2B+4x%5E3++%2B+16x+%2B+x%5E2%2B+4+
f%28x%29+=+%283x%5E4%2B+12x%5E2%29+%2B+%284x%5E3++%2B+16x+%29%2B+%28x%5E2%2B+4%29+
f%28x%29+=+3x%5E2%28x%5E2%2B+4%29+%2B+4x%28x%5E2++%2B+4+%29%2B+%28x%5E2%2B+4%29+
f%28x%29=%283x%5E2%2B4x%2B1%29%28x%5E2%2B4%29
f%28x%29=%283x%5E2%2B3x%2Bx%2B1%29%28x%5E2%2B4%29
f%28x%29=%28%283x%5E2%2B3x%29%2B%28x%2B1%29%29%28x%5E2%2B4%29
f%28x%29=%283x%28x%2B1%29%2B%28x%2B1%29%29%28x%5E2%2B4%29
f%28x%29=%28x%2B1%29%283x%2B1%29%28x%5E2%2B4%29
zeros:
%28x%2B1%29%283x%2B1%29%28x%5E2%2B4%29=0
if %28x%2B1%29=0=>x=-1
if %283x%2B1%29=0=>3x=-1=>x=-1%2F3
if %28x%5E2%2B4%29=0=>x%5E2=-4=>x=sqrt%28-4%29=>x=2i and x=-2i