Test Session Chapter 9 Division of Polynomials (1st Year Mathematics)

Multiple Choice Questions (MCQs)

Short Answer Questions

Polynomial Division Concepts

Remainder Theorem:

If P(x) is divided by (x – a), then remainder = P(a)

P(a) = remainder

Factor Theorem:

(x – a) is a factor of P(x) if and only if P(a) = 0

If P(a) = 0, then (x – a) is a factor

Synthetic Division:

Shortcut for dividing by (x – a)

Bring down, multiply, add, repeat

Long Division:

Divide, multiply, subtract, bring down

Similar to numerical long division

Percentage Error:

\% Error = \frac{|Observed – Predicted|}{Observed} \times 100\%

Zero/Root of Polynomial:

Value of x where P(x) = 0

If P(a) = 0, then x = a is a root

Remainder Theorem Calculator

Polynomial P(x):

Divisor (x – a):

Synthetic Division Calculator

Coefficients (highest to lowest):

Divisor (x – a):

Detailed Answer Questions

Question 1 (5 marks)

Use synthetic division to find the quotient and the remainder when the polynomial \(x^4 – 10x^2 – 2x + 4\) is divided by \(x + 3\).

Question 2 (5 marks)

Consider a data set at monthly sales figures. A polynomial regression model \(P(x) = x^3 + 2x^2 + x – 3\) is fitted to this data. If the observed sales in the 5th month are 240 units, find the percentage error.

Question 3 (5 marks)

Using synthetic division, show that \(x = -3\) is a zero of the polynomial \(P(x) = 2x^3 + 7x^2 + 2x – 3\). Then, use the result to factorize the polynomial completely.

Note: Answer any 2 questions. Each question carries 5 marks.

Your Score: 0 / 10