Using Division and the Factor Theorem to Factor Polynomials Worksheets (with solutions)

A collection of three worksheets on the following topics:

• Dividing polynomials using long division
• Using division to factor polynomials
• Factorising a polynomial using the factor theorem

In the first worksheet, students are required to perform long division for some given pairs of polynomials.
In the second worksheet, students must use polynomial division to find the remaining linear factors of a polynomial, given one of its factors. In other exercises, students must find a polynomial using multiplication given all its factors, find the highest common factor of given algebraic expressions and find missing terms in factorized expressions.
In the third worksheet, students are required to check whether a given polynomial is a factor of another polynomial by using the factor theorem and then in some other exercises they are required to factor cubic polynomials by first finding one of its linear factors (by checking given polynomials or inspecting using the factor theorem) and then using long division to find the remaining linear factors.
Detailed solutions are included.