Algebraic Polynomials & Identities Questions with Solutions

A polynomial is an algebraic expression made of terms with non-negative whole-number powers of a variable. This topic covers the degree and zeros of a polynomial, the remainder and factor theorems, factorisation, and standard algebraic identities such as (a + b)^2, (a - b)^2, a^2 - b^2, (a + b)^3, a^3 + b^3 and a^3 + b^3 + c^3 - 3abc. Identities are among the biggest time-savers in aptitude. Questions that seem to need heavy calculation, such as evaluating x^3 + 1/x^3 when x + 1/x is known, become one-line answers when the right identity is used. The remainder theorem similarly lets you find a remainder without long division: the remainder when p(x) is divided by (x - a) is p(a). Practise the polynomial and identity questions below, each with a step-by-step solution.