Chapter 2: Polynomials and Factorisation

Exercise 2.1

• Q1: Find the degree of the polynomial $x^5 - x^4 + 3$.

  • Solution: The highest exponent of variable $x$ is $5$. Thus, the degree is 5.

• Q2: Classify $x^2 + x$ as linear, quadratic, or cubic.

  • Solution: The degree of the expression is $2$, so it is a quadratic polynomial.

Exercise 2.2

• Remainder Theorem: If a polynomial $p(x)$ is divided by $(x - a)$, the remainder is $p(a)$.

• Factor Theorem: $(x - a)$ is a factor of $p(x)$ if and only if $p(a) = 0$.