We know that if qx divides px completely, that means px is divisible by qx or, qx is a factor of px. If \pc0\, then the remainder theorem tells us that if p is divided by \xc\, then the remainder will be zero, which means \xc\ is a factor of \p\. A lesson on the factor theorem and completely factoring a polynomial. Linear factors with a leading coefficient equal to 1.
The next theorem restates this fact in a more useful way. Factor theorem is usually used to factor and find the roots of polynomials. Students will practice using the factor theorem to determine if a linear binomial is a factor of a polynomial function. The remainder and factor theorem solving and simplifying polynomials in our study of quadratics, one of the methods used to simplify and solve was factorisation. The remainder and factor theorems were surely known to paolo ru. Mathematics support centre,coventry university, 2001 mathematics support centre title. Remainder theorem and factor theorem worksheets teaching. Given a factor and a thirddegree polynomial, use the factor theorem to factor the polynomial. Remainder and factor theorems 317 subtract from by changing the sign of each term in the lower expression and adding. To combine two reallife models into one new model, such as a model for money spent at the movies each year in ex. Use polynomial division in reallife problems, such as finding a production level that yields a certain profit in example 5. Factoring a polynomial of the 2 nd degree into binomials is the most basic concept of the factor theorem. The expression x 3 x 2 10 x 8 can now be expressed in factored form x 3 x 2 10 x 8.
That would be like factoring 740 and discovering 3 isnt a factor but then checking if anything 740 breaks down into has a factor of 3. Remainder theorem and factor theorem remainder theorem. State the possible rational zeros for each function. Divide the first term of by the first term of the divisor. These are three tiered worksheets on the remainder theorem and the factor theorem, starts off very basic, and ending with problem solving questions.
For example, we may solve for x in the following equation as follows. A root or zero is where the polynomial is equal to zero. In this algebra iicollege level worksheet, learners use long and synthetic division to divide polynomials and use the factor theorem to show that a given polynomial is a factor of a polynomial function. State whether the binomial is a factor of the polynomial 6. Hence, it can be concluded that the factor theorem is the reverse of remainder theorem. Lets take a look at how i arrived to this conclusion. On completion of this worksheet you should be able to use the remainder and factor theorems to find factors of polynomials. As you may recall, all of the polynomials in theorem 3. To use synthetic division, along with the factor theorem to help factor a polynomial. Before look at the worksheet, if you would like to know about remainder theorem and factor theorem in detail, please click here.
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. Use synthetic division to divide the polynomial by latex\leftxk\rightlatex. Worksheets are the remainder theorem, a26 mathematics support centre, remainder and factor theorems work, work polynomials, dividing polynomials remainder and factor theorems, the remainder and factor synthetic division, remainder theoremfactor theorem work, the factor theorem and the. We learned that if c is a zero of p, than x c is a factor of px. Use the remainder theorem to find the remainder for each division. The remainder and factor theorems divide using synthetic division. Remember, we started with a third degree polynomial and divided by a rst degree polynomial, so the quotient is a second degree polynomial. To learn the connection between the factor theorem and the remainder theorem 2. List all possible rational zeros of the polynomials below. Then, divide the polynomial by x minus the value 1 f x. Use the factor theorem to solve a polynomial equation.
Showing top 8 worksheets in the category factor theorem. To learn how to use the factor theorem to determine if a binomial is a factor of a given polynomial or not. C z pmcaldheu ywviatfh h yicnqfhiqn zi7t9e1 ua hltg. Worksheets are a26 mathematics support centre, remainder and factor theorems work, the remainder theorem, work polynomials, the remainder and factor synthetic division, remainder theoremfactor theorem work, the remainder theorem, more on factors zeros and dividing. Use synthetic division to evaluate 3x4 2x2 5x 1 when x 3 a. Detailed typed answers are provided to every question. 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. Students would use the remainder theorem to find the remainder when a polynomial is divided by xa withou. 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. Use the binomials that are factors to write a factored form of the original function. Write the polynomial as the product of latex\leftxk\rightlatex and the quadratic quotient. The solutions are used to navigate through the maze. Use synthetic division to find the remainder of x3 2x2 4x 3 for the factor x 3.
Click on popout icon or print icon to worksheet to print or download. Some bits are a bit abstract as i designed them myself. This is a quick inclass exercise on factor and remainder theorem worksheet with additional exercise. Bring down 21 from the original dividend and add algebraically to form a new dividend. Use the factor theorem to determine which expression is a factor of the following polynomial. The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial. Displaying all worksheets related to polynomial remainder theorem. State if the given binomial is a factor of the given polynomial. Note that the remainder theorem doesnt give you the quotient.