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# Algebra/Polynomial

Question
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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Algebra

Volunteer

#### Scott A Wilson

##### Expertise

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

##### Experience

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

Publications
Documents at Boeing in assistance on the manufacturiing floor.

Education/Credentials
MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

Awards and Honors
Both my BS and MS degrees were given with honors.

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Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.