Find a answers as a repetitions your answers as a commasepar

Find a answers as a repetitions.) your answers as a comma-separated list. Enter all answers including repetitions (Enter P(x) x4 4x3 20 4x 21

Solution

P(X) = x^4 -4x^3 -20x^2 -4x -21

The factor of the leading coefficient (1) is 1 .The factors of the constant term (-21) are 1 3 7 21 . Then the Rational Roots Tests yields the following possible solutions:

±1/1, ±3/1, ±7/1, ±21/1

Checking on all these points P(x), we obtain P(3)=0.

Divide P(x) with x+3 :  ( x^4 -4x^3 -20x^2 -4x -21)/(x +3) = x^37x^2+x7

Factorise :   x^37x^2+x7 = x^2( x-7) +1(x-7) = (x^2 +1)(x-7)

So,

P(X) = x^4 -4x^3 -20x^2 -4x -21 = (x+3)(x^2 +1)(x-7) =0

x = -3, i ,- i , 7