Question

Please answer:..........​

Answer 1

Solution:

Let p(x) = 2x³-9x²+x-12

i) p(-1) = 2(-1)³-9(-1)²+(-1)-12

= 2(-1)-9×1-1 -12

= -2-9-1-12

= -24

≠0

p(-1) ≠ 0 ,

Therefore,

(x+1) is not a factor of p(x)

ii) p(3/2)

= 2(3/2)³-9(3/2)²+(3/2)-12

= 2×(27/8)-9×(9/4)+3/2-12

= (27/4-81/4)+3/2-12

= 54/4 + 3/2-12

= 27/2+3/2-12

= (27+3-24)/2

= (30-24)/2

= 6/2

= 3

≠0

p(3/2)≠0

Therefore,

(2x-3) is not a factor of p(x)

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