Question

A polynomial p(x) is obtained by multiplying a quadratic and a cubic polynomial. What

can be the maximum number of terms in p(x)?​

Answer 1

Answer:

• Polynomials represent the next level of algebraic complexity after quadratics. Indeed a quadratic is a polynomial of degree 2. We can factor quadratic expressions, solve quadratic equations and graph quadratic functions, the obvious question arises as to  how these things might be performed with algebraic expressions of higher degree.

Step-by-step explanation:

• The quadratic x2 − 5x + 6 factors as (x − 2)(x − 3). Hence the equation x2 − 5x + 6 = 0  has solutions x = 2 and x = 3.

• Similarly we can factor the cubic x3 − 6x2 + 11x − 6 as (x − 1)(x − 2)(x − 3), which enables us to show that the solutions of x3 − 6x2 + 11x − 6 = 0 are x = 1, x = 2 or x = 3. In this module we will see how to arrive at this factorisation.

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