I have this equation: = x(20x^3 + 48x^2 + 36x + 8) I need to simply it more to f
ID: 3410496 • Letter: I
Question
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.
Explanation / Answer
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