Answer: (x + 1) is a factor of [tex]2x^{3} +x^{2} -4x -3[/tex]
Step-by-step explanation: Trying synthetic division using possible factors of the coefficients and constant, 2,4, -1, 3, -3 We find that x = -1 will work.
-1 | 2 1 -4 -3
| -2 +1 +3 When the remainder is 0, it means that the x-value tried is OK
2 1 -3 0 First three will be the coefficients of the remaining factor
[tex]2x^{3} +x^{2} -4x -3[/tex] ÷ [tex](x + 1)[/tex] Using results from synthetic division results in
[tex]2x^{2}-1x -3[/tex] This could be factored further, that would be
(2x - 3)( x + 1)
final factorization : (x + 1)(x +1)(2x +3)
