📚 Back
📚 MATHSKILLER TEXTBOOK SERIES
07

Polynomials

© 2025 MathsKiller
CHAPTER 7

Polynomials

🎯 Learning Objectives

7.1
Remainder Theorem
Remainder when $f(x)$ is divided by $(x-a)$ is $f(a)$
Example 1

Find the remainder when $f(x) = x^3 - 2x^2 + 3x - 5$ is divided by $(x-2)$.

📝 Solution

Remainder $= f(2) = 8 - 8 + 6 - 5 = 1$

7.2
Factor Theorem
$f(a) = 0 \Longleftrightarrow (x-a)$ is a factor of $f(x)$

⚡ Finding Factors

Try factors of the constant term: $\pm 1, \pm 2, \pm 3, ...$

📋 DSE Past Paper Questions

DSE 2021 Q6

If $f(x) = x^3 - kx + 6$ is divisible by $(x-2)$, find $k$.

📝 Solution

$f(2) = 8 - 2k + 6 = 0$ → $k = 7$

📝 Practice Questions

1. Find the remainder when $x^3 + 2x^2 - x + 3$ is divided by $(x-1)$.
2. Show that $(x+2)$ is a factor of $x^3 + x^2 - 4x - 4$.

📋 Answers

1. 5   2. $f(-2) = 0$ ✓

📘 MathsKiller Textbook Series | Chapter 7: Polynomials

© 2025 MathsKiller