I have this equation x20x3 48x2 36x 8 I need to simply i

I have this equation: = x(20x^3 + 48x^2 + 36x + 8)

I need to simply it more to find the roots or where it equals zero. The answer is given but I don\'t understand how they are factoring it. This is what they give as a factoring of the above equation:

= x(x + 1)(20x^2 + 28x + 8)

I see that they factored out an \'x\' but I don\'t know how to factor out \'x + 1\' from a polynomial. Can someone please explain how this is done? Math is difficult for me, please show the steps/work involved so I can better understand. Thank you.

Solution

Synthetic division helps find zeros of polynomials. F(c) = 0 if and only if the residue in the synthetic division between x-c is 0.

Since the divisor is x + 1 = x - (- 1), the value of c in the expression x-c is -1; therefore synthetic division takes this form:

-1|     20     48    36     8

      ____-20   -28    -8

          20    28     8      0

The first three digits of the third row are the coefficients of the quotient q (x) and the last number is the residue r.

(20x^2+28x+8)(x+1)x