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. Some bits are a bit abstract as i designed them myself. Remainder theorem and factor theorem remainder theorem. Siyavulas open mathematics grade 12 textbook, chapter 5 on polynomials covering remainder theorem. Recall from the previous section that a monomial is a single term, such as 6x3 or 7. The expression x 3 x 2 10 x 8 can now be expressed in. Use the factor theorem to determine which expression is a factor of the following polynomial. The terms quotient and remainder are introduced through this familiar environment before progressing to automated algebraic computations and powerful visuals to help students gain a much better conceptual understanding of polynomial division, in particular the factor and. Showing top 8 worksheets in the category factor theorem.
State if the given binomial is a factor of the given 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. The remainder factor theorem is actually two theorems that relate the roots of a polynomial with its linear factors. Remainder is 0 remainder theorem quotient is a factor of fx depressed polynomial depressed polynomial is also a factor of fx 1.
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. Mathematics support centre,coventry university, 2001 mathematics support centre title. Students are given pairs of polynomials and integer values. State whether the binomial is a factor of the polynomial 6. You may also have discovered in the activity that synthetic substitution gives the coefficients of the quotient. Use synthetic division to find the remainder of x3 2x2 4x 3 for the factor x 3. Use the remainder theorem to find the number of tickets sold during the twelfth game of the northside high school football season. Here the remainder is zero thus we can say 5 is a factor of 25 or 25 is a multiple of 5. In the case of divisibility of a polynomial by a linear polynomial we use a well known theorem called remainder theorem. Students would use the remainder theorem to find the remainder when a polynomial is divided by xa withou. 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.
On completion of this worksheet you should be able to use the remainder and factor theorems to find factors of polynomials. We learned that if c is a zero of p, than x c is a factor of px. This is a quick inclass exercise on factor and remainder theorem worksheet with additional exercise. Using the above theorem and your results from question. In this section we will learn how to divide polynomials, an important tool needed in factoring them. As you may recall, all of the polynomials in theorem 3. 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. 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. Displaying top 8 worksheets found for factor theorem. Note that the remainder theorem doesnt give you the quotient. C z pmcaldheu ywviatfh h yicnqfhiqn zi7t9e1 ua hltg. 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. Corollary the factor theorem a polynomial fx has x as a factor if and only if f. Create your own worksheets like this one with infinite algebra 2.
Divide polynomials and relate the result to the remainder theorem and the factor theorem. Especially when combined with the rational root theorem, this gives us a powerful tool to factor polynomials. Worksheet by kuta software llc precalculus rchen 2. List all possible rational zeros of the polynomials below. 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. About the lesson this activity starts with familiar skills, terminology and concepts relating to division of whole numbers. Divide the first term of by the first term of the divisor. 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. Use polynomial division in reallife problems, such as finding a production level that yields a certain profit in example 5. Apr 15, 2014 the worksheet also allows students to apply the factor and remainder theorem to factors and divisors.
Each possible rational zero should then be tested using synthetic division. Unit 4 worksheet 2 the remainder theorem when trying to find all zeros of a complex polynomial function, use the rational zero test to find all possible rational zeros. This packet includes the remainder and factor theorem study guide and answer key. This will begin our algebraic study of polynomials. Using the binomials you determined were factors of. This result is generalized in the 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\. Eleventh grade lesson the remainder theorem betterlesson. Detailed typed answers are provided to every question. Why you should learn it goal 2 goal 1 what you should learn. 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. Showing top 8 worksheets in the category factor and remainder theorem.
Section 4 the factor theorem and roots of polynomials. 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. My students will practice using the remainder theorem by completing ws solving polynomials with the remainder theorem with their table partners. D d pmpaxd 2eo bw 6i ktfh y ei znxfoi onsi nt wet ja 1lvgheubvr va x f2 e. Use polynomial division in reallife problems, such as finding a. 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. Lets learn about the remainder theorem of polynomials. Use synthetic division to evaluate 3x4 2x2 5x 1 when x 3 a. The worksheet also allows students to apply the factor and remainder theorem to factors and divisors. The theorem is often used to help factorize polynomials without the use of long division. If x a is substituted into a polynomial for x, and the remainder is 0, then x. Remember, we started with a third degree polynomial and divided by a rst degree polynomial, so the quotient is a second degree polynomial. This worksheet contains 4 challenging problems in which students use the remainder theorem to identify a root, divide it out using long division, and then find the zeros of the quotient polynomial mp1. Displaying all worksheets related to remainder theorem.
Use the factor theorem to solve a polynomial equation. The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial. The next theorem restates this fact in a more useful way. It is a special case of the remainder theorem where the remainder 0. They are instructed to first substitute the value in for x in the polynomial and then divide out the factor associated with that value. If x a is substituted into a polynomial for x, and. 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\. The remainder theorem states \p2\ is the remainder when \px\ is divided by \x2\. The expression x 3 x 2 10 x 8 can now be expressed in factored form x 3 x 2 10 x 8. The remainder theorem is a short cut to find the remainder of polynomial long division or synthetic division. Remainder and factor theorems precalculus socratic. Resource on the factor theorem with worksheet and ppt. The remainder and factor theorems divide using synthetic division. Since there is a remainder when the cubic is divided by x.
When we divide a number, for example, 25 by 5 we get 5 as quotient and 0 as the remainder. The remainder theorem told us that if px is divided by x. Remainder theorem and factor theorem onlinemath4all. Given a number 3, dividing by x3 leaves quotientdepressed polynomial x23x4 3 1 6 5 12 remainder is 0 so its a. Polynomial remainder theorem proof and solved examples. Synthetic division in this section you will learn to. If one of these numbers work, there will be no remainder to the division problem. Before look at the worksheet, if you would like to know about remainder theorem and factor theorem in detail, please click here. To combine two reallife models into one new model, such as a model for money spent at the movies each year in ex. Use the remainder theorem to find the remainder for each division. In this section, we shall study a simple and an elegant method of finding the remainder.
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