Question

check whether x+3 is a factor of x³+2x²-5x-6 or not.​

Answer 1

using remainder theorem

put p(x)= -3

p(-3) = -3³+2(-3)²-5(-3)-6

= -27-18+15-6

= 33-33

= 0

therefore, x+3 is factor of p(x)

Answer 2

• [{x}^{3} + 2x {}^{2} - 5x - 6 = 0 \\ {x}^{3} + {x}^{2} + {x}^{2} - 5x - 6x = 0 \\ {x}^{2} (x + 1) + {x}^{2} - 5x - 6 = 0 \\ {x}^{2} (x + 1) + {x}^{2} + x - 6x - 6 = 0 \\ {x}^{2} (x + 1) + x(x + 1) - 6(x + 1) = 0 \\ (x + 1)( {x}^{2} + x - 6) = 0 \\ (x + 1)( {x}^{2} + 3x - 2x - 6) = 0 \\ (x + 1)(x(x + 3) - 2(x +3)) = 0 \\ (x + 1)(x + 3)(x - 2) = 0 \\ x + 1 = 0 \\ x = - 1 \\ x + 3 = 0 \\ x = - 3 \\ x - 2 = 0 \\ x = 2