# Applying the Remainder Theorem Worksheets

This is a method that you can use to avoid overly excessively long division of polynomials. Those types of calculations can use up a ton of paper and be very complicated. This can become very useful when evaluating graphs of polynomials, it gives a quick way to understand if a factor is being applied or is present at all. They ultimately allow you to decide if a linear expression is a factor of a polynomial expression. You can also pair this with synthetic division to really chop through them quickly and evaluate polynomials at fixed locations. These worksheets help students understand and apply the math shortcut known as the remainder theorem.

### Aligned Standard: HSA-APR.B.2

- Quotient Remainders Step-by-step Lesson-Use the remainder theorem to find the remainder of a this polynomial that id divided by two.
- Guided Lesson - The lesson starts with a whole number divisor. We move on to dividing by binomials.
- Guided Lesson Explanation - We show you how these problems are nowhere near as hard as they look.
- Practice Worksheet - Start working away at find the remainders to these quotients.
- Matching Worksheet - Match the problems to their missing remainders.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

We are more focused on the remainder than the actual quotient here.

- Homework 1 - In algebra, the remainder theorem is an application of polynomial long division. It states that the remainder of a polynomial f(x) divided by a linear divisor (x – c) is equal to f(c).
- Homework 2 - We know the remainder after dividing by k-c we don't need to do any division. We have to just calculate f(k).
- Homework 3 - Find the remainder of each problem below.

### Practice Worksheets

I tried to use light exponents here. But I got a little more challenging in version 3.

- Practice 1 - We follow the same format once again.
- Practice 2 - (k
^{2}– 20k – 11) ÷ k - 4) - Practice 3 - Put it all together.

### Math Skill Quizzes

I made the divisors follow a pattern here to make sure that they built as you went on.

- Quiz 1 - Smash this thing all together.
- Quiz 2 - Why not put all the things to the side.
- Quiz 3 - Removing pieces of the whole makes a difference.

### What is the Remainder Theorem?

Linear and quadratic equations are very easy to solve. You can use the substitution method or the elimination method for solving a system of linear equations. For the quadratic equation, you may use the quadratic formula, completing-the-square method, and middle-term break methods.

So, what do you do if there is a cubic equation or any higher power polynomial? Well, when it comes to solving higher power polynomials, you may use the remainder theorem. The remainder theorem allows you to evaluate a polynomial at any given value of x.

The theorem revolves around dividing a polynomial with a linear factor. The result of this division is a quotient polynomial. It reduces the power of the polynomial, which you can solve with simpler methods, and it gives you the remaining values of x. In general, if you divide a polynomial by a binomial there will be a remainder. The remainder theorem tells us if a polynomial described as f(x) is dividing by x - a, the remainder is the constant f(a). it also tells us that f(x) = b(x) * (x - a) + f(a), b(x) is the polynomial with a degree that is one less than the degree of f(x).

The linear factor is a result of trial-and-error methodology if it's not provided in the question.

Consider a cubic expression; p(x) = x^{3} - 7x - 6

And you have to divide it by x - 4. You can now solve the quadratic equation and find out the other two values of x. It is all about determine which term is applicable within the theorem.