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Sir, how to solve polynomial world problem. For example,  The polynomial 2x^3+qx^2+rx+2 has a factor (x-1) and leaves a remainder of 12 when divided by (x-2). Find the constants q and r and hence the other factors of the polynomial.

Multiplying this by x-1 gives 2x^3 + (a-2)x^2 + (-a-2)x + 2.

To have a factor x-1, the result should start with 2x^2 and end with -2.
This makes the factor 2x^2 + ax - 2.

Divide x-2 into 2x^2 + ax - 2.  Multiply by 2x, giving 2x^2-4x, and subtract,
This gives (4+a)x - 2 as the remainder so far.

Now we multiply by 4+a, giving (4+a)x - 8 - 2a, and subtract.
This gives 6 + 2a.  Since this is 12, subtracting 6 from both sides gives 2a = 6.
This says a is 3.

This gives 2x^3 + x^2 - 5x + 2.
Dividing by x-1 gives (x-1)(2x^2 + 3x - 2).

That factors into (2x-1)(x+2).

Solving 2x-1=0 and x+2=0 gives the solutions.
Multiplying it out will give the values of q and r.  


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Scott A Wilson


Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.


I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

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