Polynomial relationship problem

In summary, for part a), the remainder when q(x) is divided by x-2 can be found by using the idea that if a polynomial p(x) has a root at a=0, then p(a)=0. For part b), the values of a and b can be found by establishing an equation with the two unknowns using the same idea and using the answer from part a) to find another equation and solve them simultaneously.
  • #1
Michael_Light
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0

Homework Statement



Polynomials p(x) and q(x) are given by relationship q(x)=p(x)(x5-2x+2).

a) If x-2 is a factor of p(x)-5 , find the remainder when q(x) is divided by x-2.

b) If p(x) is of the form x2+ax+b and x-1 is a factor of p(x)-5, find the values of a and b.


Homework Equations





The Attempt at a Solution



Can anyone help? :frown:
 
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  • #2


For -

a) use the idea that if a polynomial p(x) has a root at a=0, then p(a)=0

b) Using the same idea as above, you should be able to establish an equation with the two unknowns a and b in it. To find another equation so that you can solve them simultaneously, use your answer from a).
 

FAQ: Polynomial relationship problem

1. What is a polynomial relationship problem?

A polynomial relationship problem is an algebraic problem that involves finding the relationship between two or more variables, represented by polynomial equations. These equations contain terms with variables raised to different powers, such as x^2 or x^3, and may also include constants. The goal is to solve for the variables and determine the relationship between them.

2. How do you solve a polynomial relationship problem?

To solve a polynomial relationship problem, you can use a variety of methods, such as substitution, elimination, or graphing. These methods involve manipulating the equations and using algebraic techniques to solve for the variables. It is important to follow the order of operations and be careful with signs and exponents when solving these types of problems.

3. What is the degree of a polynomial relationship?

The degree of a polynomial relationship refers to the highest exponent in the equation. For example, a polynomial equation with x^3 as the highest exponent has a degree of 3. The degree can also help determine the complexity of the relationship and the number of solutions it may have.

4. How do you know if a polynomial relationship has real solutions?

A polynomial relationship will have real solutions if its graph intersects the x-axis at one or more points. This means that there are values of the variables that satisfy the equation and make it true. If the graph does not intersect the x-axis, then there are no real solutions.

5. What are some real-world applications of polynomial relationships?

Polynomial relationships have many real-world applications in fields such as physics, engineering, and economics. They can be used to model and predict the behavior of physical systems, such as the motion of objects or the growth of populations. In economics, polynomial relationships can be used to analyze and make predictions about market trends and consumer behavior.

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