SOLUTION: Please help me solve this. Find all zeros of the function and write the polynomial as a product of linear factors. f(x)=3x^4+4x^3+13x^2+16x+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this. Find all zeros of the function and write the polynomial as a product of linear factors. f(x)=3x^4+4x^3+13x^2+16x+4      Log On


   

Question 976987: Please help me solve this.
Find all zeros of the function and write the polynomial as a product of linear factors.
f(x)=3x^4+4x^3+13x^2+16x+4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=3x%5E4%2B4x%5E3%2B13x%5E2%2B16x%2B4.........write 13x%5E2 as x%5E2%2B12x%5E2
f%28x%29=3x%5E4%2B4x%5E3%2Bx%5E2%2B12x%5E2%2B16x%2B4...........group
f%28x%29=%283x%5E4%2B12%29%2B%284x%5E3%2B16x%29%2B%28x%5E2%2B4%29
f%28x%29=3x%5E2%28x%5E2%2B4%29%2B4x%28x%5E2%2B4%29%2B%28x%5E2%2B4%29
f%28x%29=%283x%5E2%2B4x%2B1%29+%28x%5E2%2B4%29+
f%28x%29=%283x%5E2%2Bx%2B3x%2B1%29+%28x%5E2%2B4%29+
f%28x%29=%28%283x%5E2%2Bx%29%2B%283x%2B1%29%29+%28x%5E2%2B4%29+
+f%28x%29=%28x%2B1%29+%283x%2B1%29+%28x%5E2%2B4%29+
zeros:
+0=%28x%2B1%29+%283x%2B1%29+%28x%5E2%2B4%29+
+0=%28x%2B1%29++=>x=-1
+0=+%283x%2B1%29+=>3x=-1=>x=-1%2F3
and, since %28x%5E2%2B4%29=0=>x%5E2=-4=>x=sqrt%28-4%29=>and zeros are x=2i or x=-2i,
then %28x%5E2%2B4%29=%28x-2i%29%28x%2B2i%29
and our the polynomial as a product of linear factors is:
f%28x%29=%28x%2B1%29+%283x%2B1%29%28x-2i%29%28x%2B2i%29