Question 1127716
<br>
0 can't be a root; if it were, the constant term would be 0.<br>
Test 1 and -1 by evaluating the polynomial at those values.  It turns out f(1)=0 and f(-1)=0, so both are roots.  Roots of 1 and -1 correspond to binomial factors of x-1 and x+1; factor them out by factoring, long division, synthetic division, or any other method you know.<br>
x^4-4x^3-22x^2+4x+21 = (x-1)(x+1)(x^2-4x-21)<br>
The remaining quadratic is easily factored:<br>
x^4-4x^3-22x^2+4x+21 = (x-1)(x+1)(x-7)(x+3)<br>
The roots are 1, -1, -3, and 7.