Factor the polynomial using synthetic division. 2x^3-3x^2-8x-3

Answer 1

Using synthetic division you are only concerned with the coefficients and the remainder. If the remainder is zero, it is a root of the equation. So let’s begin:

-1. 2. -3. -8. -3

-2. 5. 3

2. -5. -3. 0. The remainder is 0.

So so the answer is (x+1)(2x^2 -5x -3)

Answer 2

Using Rational Zero Theorem we have possible rational zeros: 1, -1, 3, -3, 1/2, -1/2, 3/2,-3/2. Using Synthetic division we see -1, 3, -1/2 arec zeros. Then by factoring Theorem we have:2x^3 - 3x^2-8x-3 =

= 2(x+1)(x-3)(x+1/2) =(x+1)(x-3)(2x+1)