Question

using remainder theorm factorize 2xcube + xsquare -13x +6

Answer 1

Since this equation could have roots of ±1,±2,±3, or ±6 as well as fractions of ±1/2 or ±3/2, try synthetic division by one of these numbers looking for a zero remainder.
. ___________
1)2 1 -13. . 6
.__2__3_-10_
. 2. 3 -10 . -4 <=with a remainder of -4, 1 is not a root

. ___________
2)2 1 -13 . 6
.__4_10_-6_
. 2. 5. -3 . 0 <=with a remainder of 0, so x = 2 is a root and x - 2 is a factor

2x³ + x² - 13x + 6 factors into (x - 2)(2x² + 5x - 3)

(2x² + 5x - 3) factors into (2x - 1)(x + 3)

So, 2x³ + x² - 13x + 6 factors into (x - 2)(2x - 1)(x + 3) <==ANSWERS

I hope that helps!! :-)