Basic Factorisation

The video tutorial covers the concept of factorization, starting with natural numbers and extending to algebraic expressions. It explains how to break down numbers and expressions into their factors, highlighting the difference between prime and irreducible factors. The tutorial introduces two main methods for factorizing algebraic expressions: using common factors and regrouping terms. Examples are provided to illustrate each method, demonstrating how to identify and extract common factors to simplify expressions.

What is the factorization of the number 36?

• 6 times 6

• 18 times 2

• 12 times 3

• 9 times 4

In algebra, what are irreducible factors?

• Factors that can be further divided

• Factors that are prime numbers

• Factors that are only numbers

• Factors that cannot be further factorized

Which of the following expressions can have its factors read directly?

• 3x + 6

• 5a + 5b

• 3ab

• p^2 + 8p + 15

What is the first step in the method of common factors?

• Regrouping terms

• Finding a common factor for all terms

• Writing each term as a product of irreducible factors

• Adding terms together

In the expression 12p^2q + 15pq^2, what are the common factors?

• 3, p, q

• p^2, q^2

• 12, p, q

• 15, q

What is the key step in factorization by regrouping terms?

• Multiplying all terms together

• Changing the order of terms to find common factors

• Finding a common factor for all terms

• Dividing terms by a common factor

In the expression 3pq + 3q + 5p + 5, what is the common factor after regrouping?

• 3pq

• 5

• 3q

• p + q