Question

p(x) = 4x^3+12x^2+11x-5, q(x) = x-1/2​

Answer 1

Answer:

$(x-\frac{1}{2} )(4x^2+14x+18)+4=4x^3+12x^2+11x-5$

Refer to the attachment, to get your answer.

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Answer 2

Answer:

If we have to check whether q(x) is a factor of p(x) then we can check it using factor theorem....

p(-1/2) = 4 ( -1/2 )³ + 12 (-1/2)² +11 ( -1/2 ) - 5

= -1/2 + 3 - 11/2 - 5

= (-1 +6 -11 - 10) / 2

= -18 / 2

= -9.........

Hence q(x) is not a factor of p(x)....

but the remainder will be -9