You are here:

- Home
- Science
- Math for Kids
- Algebra
- Polynomial

Advertisement

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.

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | Wow!! The great mathematics Ace! |

Algebra

Answers by Expert:

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.
**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.
**Past/Present Clients**

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