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+2
Answers
Answer:
(1)
Step-by-step explanation:
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(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