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I have tried all i could to solve polynomial_linear_word_problem. however, no avail. For example, the remainder when the polynomial p(x)=gx^3+hx^2+12x+27 is divided by (x-1) is 5, and when it is divided by (x+1) the remainder is -17. Determine the values of g and h. Please sir, ellucidate and solve this question for me to deepen my understanding. And be able to solve any complicated "polynomial-linear-word-problem"

You need to be able to do long division of polynomials to solve this problem, something you'll need get from your course work or a textbook. Given that ability, then I get the remainders as

(gx^3+hx^2+12x+27)/(x-1)

= 27-12-h-g = 5 and

(gx^3+hx^2+12x+27)/(x+1)

= 27+12-h+g = -17

where you'll notice that the numbers 5 and -17 are the remainder given in your problem.

These are 2 independent equations in the 2 unknowns, g and h, that you can solve. I get g = -23 and h = -13, but you should work through it yourself since it is highly likely I made an arithmetic error somewhere.

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