Using remainder factor theorem

Thread starter Terrell
Start date Dec 3, 2016
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Remainder Theorem

In summary, the remainder factor theorem is a mathematical theorem that states that when dividing a polynomial by a linear binomial, the remainder is equal to the value of the polynomial at the binomial's root. It is used to find the factors of a polynomial and can be used with any polynomial function, though it is most commonly used with quadratic functions. The steps for using the remainder factor theorem include writing the polynomial in standard form, identifying the linear binomial, setting it equal to zero and solving for x, and substituting the value of x into the polynomial to find the remainder. It can also be used to check the accuracy of long division of polynomials.

Dec 3, 2016

Terrell

1. Homework Statement
i attached the problem statement as an image file

Homework Equations

p(x) = (x-c)q(x) + r

The Attempt at a Solution

i've simplified it down to ((x-1)^114) / (2^114)(x+1). is there a practical way to approach this besides long division? wolfram alpha gave an extremely long answer

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Dec 3, 2016

Terrell

nevermind. i found it

FAQ: Using remainder factor theorem

What is the remainder factor theorem?

The remainder factor theorem is a mathematical theorem that states that when a polynomial function f(x) is divided by a linear binomial (x-a), the remainder is equal to the value of f(a). In other words, the remainder factor theorem helps us find the remainder when dividing a polynomial by a linear factor.

How is the remainder factor theorem used in solving polynomial equations?

The remainder factor theorem is used in solving polynomial equations by helping us find the factors of a polynomial. By finding the factors, we can then set them equal to zero and solve for the values of x that make the polynomial equal to zero.

Can the remainder factor theorem be used with any polynomial function?

Yes, the remainder factor theorem can be used with any polynomial function. However, it is most commonly used with quadratic functions, where the linear binomial (x-a) is a factor of the quadratic polynomial.

What are the steps for using the remainder factor theorem?

The steps for using the remainder factor theorem are as follows:
1. Write the polynomial function in standard form.
2. Identify the linear binomial (x-a) that is a factor of the polynomial.
3. Set the linear binomial equal to zero and solve for x.
4. Substitute the value of x into the polynomial function to find the remainder.

Can the remainder factor theorem be used for long division of polynomials?

Yes, the remainder factor theorem can be used for long division of polynomials. In fact, it is often used to check the accuracy of long division by comparing the remainder from the long division with the remainder found using the remainder factor theorem.