# polynomial functions & eqns (HL)

downloadable teaching materials for polynomial functions & equations
► syllabus content for the Functions & Equations Topic: HL syllabus (see syllabus section 2.5).

The syllabus items related to polynomial functions & equations are included in the HL syllabus sections 2.5, 2.6 & 2.7. Specifically this includes: polynomial functions & their graphs, factor & remainder theorems, fundamental theorem of algebra, sum & product of the roots of polynomial equations, and solving inequalities involving polynomials up to cubics (some overlap with the Solving Inequalities (HL) page on this site). [Should really be referring to this group of HL syllabus items as polynomial functions, equations & inequalities]

The sum & product of the roots of polynomial equations - although a common topic for other courses such as A-levels in the UK - was newly added to the HL syllabus in the latest revision of the HL course (first exams May 2014). One aspect about this syllabus item is that, unfortunately, the formulas for the sum & product of the roots are not provided in the HL formula booklet. I believe these formulas are the only things that I require my students to memorize (particularly for a general polynomial equation of degree n).  In teaching materials below there is an exercise set with four questions on sum & product of roots of quadratic & higher-degree polynomial equations.

### 3 questions - ‘accessible’ to ‘discriminating’

accessible HL question

moderate HL question

discriminating HL question

#### Course planning / teaching notes:

##### ♦ teaching materials

EXS_2-5-20v1_HL_factor_remainder_theorems
Set of 15 exercises (no GDC allowed) on applying the factor theorem and remainder theorem to polynomial functions (worked solutions included).

EXS_2-5-30v1_HL_polynomial_functions
Set of 15 exercises (non-calculator & calculator allowed) covering the following syllabus content: polynomial functions & their graphs, factor & remainder theorems, fundamental theorem of algebra, solving polynomial equations & inequalities both graphically & algebraically, sum & product of the roots of a polynomial equation (answers included)

EXS_2-6-50v1_HL_sum_prod_roots_poly_eqn
Set of four exam-like questions on the sum & product of roots of a quadratic or higher-degree polynomial equation (worked solutions included)

Test_HL_poly_functions_eqns_inequalities_v1
Unit test with 12 questions (60 marks) - 7 questions with no GDC, and 5 questions allowing GDC. Following syllabus items covered: polynomial functions, quadratic formula and discriminant, factor & remainder theorems, polynomial division, sum and product of roots of a polynomial equation, rational functions, solving equations involving radicals, absolute value and in quadratic form, solving inequalities (worked solutions below)

Test_HL_poly_functions_eqns_inequalities_v1_SOLUTION_KEY
Worked solutions for all questions for above unit test on polynomial functions, equations & inequalities

Test2_HL_poly_functions_eqns_ineq_v1
Unit test with 11 questions (60 marks) - 6 questions with no GDC, and 5 questions allowing GDC. The test covers the following syllabus content: polynomial functions, quadratic formula and discriminant, factor & remainder theorems, polynomial division, sum and product of roots of a polynomial equation, rational functions, solving inequalities (worked solutions below)

Test2_HL_poly_functions_eqns_ineq_v1_SOL_KEY
Worked solutions for all questions for above Test2 on polynomial functions, equations & inequalities

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