Since there is a remainder when the cubic is divided by x. Siyavulas open mathematics grade 12 textbook, chapter 5 on polynomials covering remainder theorem. Remainder theorem and factor theorem worksheets teaching. The factor theorem states that a polynomial f x has a factor x k if and only f k 0. We learned that if c is a zero of p, than x c is a factor of px. Use polynomial division in reallife problems, such as finding a. Why you should learn it goal 2 goal 1 what you should learn. Bring down 21 from the original dividend and add algebraically to form a new dividend. Use the factor theorem to solve a polynomial equation.
Remainder and factor theorems precalculus socratic. Remainder is 0 remainder theorem quotient is a factor of fx depressed polynomial depressed polynomial is also a factor of fx 1. Some of the worksheets for this concept are remainder and factor theorems work, a26 mathematics support centre, the remainder theorem, remainder theoremfactor theorem work, the factor theorem and the remainder theorem, dividing polynomials remainder and factor theorems, work polynomials, state the possible rational. To combine two reallife models into one new model, such as a model for money spent at the movies each year in ex. State if the given binomial is a factor of the given polynomial. While i check homework with the homework rubric, my students work on warmup remainder theorem, which is a worksheet i created to help students discover the pattern expressed in the remainder theorem. About the lesson this activity starts with familiar skills, terminology and concepts relating to division of whole numbers. Remainder theorem and factor theorem onlinemath4all. If one of these numbers work, there will be no remainder to the division problem. This packet includes the remainder and factor theorem study guide and answer key. The theorem is often used to help factorize polynomials without the use of long division. Displaying all worksheets related to remainder theorem.
These are three tiered worksheets on the remainder theorem and the factor theorem, starts off very basic, and ending with problem solving questions. The remainder and factor theorems divide using synthetic division. Apr 15, 2014 the worksheet also allows students to apply the factor and remainder theorem to factors and divisors. State whether the binomial is a factor of the polynomial. This grade12 caps mathematics worksheet is designed to reinforce the concepts learnt about the factor and remainder theorem as applied to polynomials particularly for factorising cubic expressions. The remainder factor theorem is actually two theorems that relate the roots of a polynomial with its linear factors. Corollary the factor theorem a polynomial fx has x as a factor if and only if f. Detailed typed answers are provided to every question. The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial. Synthetic division in this section you will learn to.
Some of the worksheets displayed are the remainder theorem, a26 mathematics support centre, remainder and factor theorems work, the remainder theorem, remainder theoremfactor theorem work, the factor theorem and the remainder theorem, dividing polynomials remainder and factor theorems, the. State whether the binomial is a factor of the polynomial 6. When we divide a number, for example, 25 by 5 we get 5 as quotient and 0 as the remainder. Remember, we started with a third degree polynomial and divided by a rst degree polynomial, so the quotient is a second degree polynomial. Worksheet given in this section will be much useful for the students who would like to practice solving problems on remainder theorem and factor theorem. Using the binomials you determined were factors of. You may also have discovered in the activity that synthetic substitution gives the coefficients of the quotient. Use the remainder theorem to find the remainder for each division.
If x a is substituted into a polynomial for x, and the remainder is 0, then x. Resource on the factor theorem with worksheet and ppt. The remainder theorem told us that if px is divided by x. Showing top 8 worksheets in the category factor and remainder theorem.
Given a number 3, dividing by x3 leaves quotientdepressed polynomial x23x4 3 1 6 5 12 remainder is 0 so its a. The worksheet also allows students to apply the factor and remainder theorem to factors and divisors. Use synthetic division to find the remainder of x3 2x2 4x 3 for the factor x 3. The next theorem restates this fact in a more useful way. Some bits are a bit abstract as i designed them myself. Before look at the worksheet, if you would like to know about remainder theorem and factor theorem in detail, please click here. The expression x 3 x 2 10 x 8 can now be expressed in. Worksheet by kuta software llc precalculus rchen 2. Divide polynomials and relate the result to the remainder theorem and the factor theorem. If x a is substituted into a polynomial for x, and. As you may recall, all of the polynomials in theorem 3. In this section, we shall study a simple and an elegant method of finding the remainder. Divide the first term of by the first term of the divisor. Use polynomial division in reallife problems, such as finding a production level that yields a certain profit in example 5.
This will begin our algebraic study of polynomials. The expression x 3 x 2 10 x 8 can now be expressed in factored form x 3 x 2 10 x 8. Some of the worksheets displayed are the remainder theorem, a26 mathematics support centre, remainder and factor theorems work, the remainder theorem, remainder theoremfactor theorem work, the factor theorem and the remainder theorem, dividing polynomials remainder and factor. Polynomial remainder theorem proof and solved examples. The remainder theorem states \p2\ is the remainder when \px\ is divided by \x2\. In this section we will learn how to divide polynomials, an important tool needed in factoring them. The factor theorem if the polynomial \px\ is divided by \cx d\ and the remainder, given by \p \left \fracdc \right,\ is equal to zero, then \cx d\ is a factor of \px\. They are instructed to first substitute the value in for x in the polynomial and then divide out the factor associated with that value. Displaying top 8 worksheets found for factor theorem.
Worksheets are the remainder theorem, a26 mathematics support centre, the remainder theorem, remainder and factor theorems work, remainder theoremfactor theorem work, the remainder theorem and bounds date period, dividing polynomials remainder and factor theorems, the factor theorem and the remainder theorem. My students will practice using the remainder theorem by completing ws solving polynomials with the remainder theorem with their table partners. Each possible rational zero should then be tested using synthetic division. The remainder theorem is a short cut to find the remainder of polynomial long division or synthetic division. Use the factor theorem to determine which expression is a factor of the following polynomial. Recall from the previous section that a monomial is a single term, such as 6x3 or 7. Lets learn about the remainder theorem of polynomials. In the case of divisibility of a polynomial by a linear polynomial we use a well known theorem called remainder theorem. Use the fact that \x1\ is a zero of \p\ to factor \px\ and then find all of the real zeros of \p\. Showing top 8 worksheets in the category factor theorem. Section 4 the factor theorem and roots of polynomials. D d pmpaxd 2eo bw 6i ktfh y ei znxfoi onsi nt wet ja 1lvgheubvr va x f2 e. Use the remainder theorem to find the number of tickets sold during the twelfth game of the northside high school football season.
It is a special case of the remainder theorem where the remainder 0. Note that the remainder theorem doesnt give you the quotient. Especially when combined with the rational root theorem, this gives us a powerful tool to factor polynomials. This is a quick inclass exercise on factor and remainder theorem worksheet with additional exercise. Some of the worksheets displayed are remainder and factor theorems work, a26 mathematics support centre, the remainder theorem, remainder theoremfactor theorem work, the factor theorem and the remainder theorem, dividing polynomials remainder and factor theorems, work polynomials, state the possible rational zeros for each. Students would use the remainder theorem to find the remainder when a polynomial is divided by xa withou.
List all possible rational zeros of the polynomials below. Students are given pairs of polynomials and integer values. The remainder theorem if is any polynomial and is divided by, then the remainder is the validity of this theorem can be tested in any of the equations above, for example. Remainder theorem and factor theorem remainder theorem. In this section, you will learn remainder theorem and factor theorem. Remainder and factor theorems 317 subtract from by changing the sign of each term in the lower expression and adding. Mathematics support centre,coventry university, 2001 mathematics support centre title. This result is generalized in the remainder theorem. Some of the worksheets displayed are remainder and factor theorems work, a26 mathematics support centre, the remainder theorem, remainder theoremfactor theorem work, the factor theorem and the remainder theorem, dividing polynomials remainder and factor theorems, work polynomials, state the possible rational. This study guide includes problems on long division, long division with a nonzero remainder, division of polynomial of degree 2 or higher, synthetic division, remainder theorem, and factor theorem. On completion of this worksheet you should be able to use the remainder and factor theorems to find factors of polynomials.