Question

user reminder theorem to find which of the following is factor of 2 x cube + 3 x square - 5 x minus 6 (i) X + 1 (ii)2x-1 (iii)x+2in attachments ​

Answer 1

(i) X + 1

Here, p(x)= 2x³+3x²-5x-6 and the zero of x + 1 is -1

p(1)=2(-1)³+3(-1)²-5(-1)-6

=-2+3+5-6

=0

So,by the remainder theorem, 0 is the reminder.

Therefore, x+1 is factor of 2x³+3x²-5x-6

(ii)2x-1

Here, p(x)= 2x³+3x²-5x-6 and the zero of 2x - 1 is 1/2

p(1/2)=2(1/2)³+3(1/2)²-5(1/2)-6

=1/4 +3/4 -5/2-6

=(1+3-10-24)/4

=-30/4

=-15/2

So,by the remainder theorem, -15/2 is the reminder.

Therefore, 2x-1 is not factor of 2x³+3x²-5x-6

(iii)x+2

Here, p(x)= 2x³+3x²-5x-6 and the zero of x + 2 is -2

p(2)=2(-2)³+3(-2)²-5(-2)-6

= -16+12+10-6

=0

So,by the remainder theorem, 0 is the reminder.

Therefore, x+2 is a factor of 2x³+3x²-5x-6

Answer 2

(i) X + 1

Here, p(x)= 2x³+3x²-5x-6 and the zero of x + 1 is -1

p(1)=2(-1)³+3(-1)²-5(-1)-6

=-2+3+5-6

=0

So,by the remainder theorem, 0 is the reminder.

Therefore, x+1 is factor of 2x³+3x²-5x-6

(ii)2x-1

Here, p(x)= 2x³+3x²-5x-6 and the zero of 2x - 1 is 1/2

p(1/2)=2(1/2)³+3(1/2)²-5(1/2)-6

=1/4 +3/4 -5/2-6

=(1+3-10-24)/4

=-30/4

=-15/2

So,by the remainder theorem, -15/2 is the reminder.

Therefore, 2x-1 is not factor of 2x³+3x²-5x-6

(iii)x+2

Here, p(x)= 2x³+3x²-5x-6 and the zero of x + 2 is -2

p(2)=2(-2)³+3(-2)²-5(-2)-6

= -16+12+10-6

=0

So,by the remainder theorem, 0 is the reminder.

Therefore, x+2 is a factor of 2x³+3x²-5x-6