What you’ll learn5 learning objectivesChoose one objective for a focused lesson, or study the complete topic.3.1.1Modulus equations• understand the meaning of |x|, sketch the graph of y = |ax + b| and use relations such as |a| = |b| ⇔ a2 = b2 and |x - a| < b ⇔ a - b < x < a + b when solving equations and inequalities Graphs of y = |f(x)| and y = f(|x|) for non-linear functions f are not included. e.g. |3x - 2| = |2x + 7|, 2x + 5 < |x + 1|.Syllabus objective3.1.2Polynomial division• divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero)Syllabus objective3.1.3Factor and remainder theorems• use the factor theorem and the remainder theorem e.g. to find factors and remainders, solve polynomial equations or evaluate unknown coefficients. Including factors of the form (ax + b) in which the coefficient of x is not unity, and including calculation of remainders.Syllabus objective3.1.4Partial fractions• recall an appropriate form for expressing rational functions in partial fractions, and carry out the decomposition, in cases where the denominator is no more complicated than - (ax + b)(cx + d)(ex + f) - (ax + b)(cx + d)2 - (ax + b)(cx2 + d) Excluding cases where the degree of the numerator exceeds that of the denominator.Syllabus objective3.1.5Binomial expansion• use the expansion of (1 + x)n, where n is a rational number and x 11. Finding the general term in an expansion is not included. Adapting the standard series to expand e.g. x2 2 1 1 - - `j is included, and determining the set of values of x for which the expansion is valid in such cases is also included.Syllabus objective