A polynomial function is defined as
f(x)=x4+ax3+2x2+bx−6 f(x) = x^4 + ax^3 + 2x^2 + bx - 6 f(x)=x4+ax3+2x2+bx−6where aaa and bbb are constants.
When f(x)f(x)f(x) is divided by (x−1)(x - 1)(x−1), the remainder is −10-10−10. Show that a+b=−7a + b = -7a+b=−7.
When f(x)f(x)f(x) is divided by (x+2)(x + 2)(x+2), the remainder is 222. Find the value of aaa and the value of bbb.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.