Factorization and Common Factors

This video tutorial introduces the concept of factorising algebraic expressions, starting with basic numbers and moving to algebraic terms. It explains how to find the highest common factor to factorise expressions and provides several examples, including complex expressions with multiple variables and higher indices. The tutorial concludes with a recap and encourages viewers to ask questions if needed.

What does factorising an algebraic expression involve?

• Adding a constant to each term

• Breaking an expression into its factors

• Multiplying all terms by a constant

• Combining terms into a single term

If you factorise the number 55, which of the following is a correct pair of factors?

• 1 and 54

• 10 and 5.5

• 5 and 11

• 2 and 27.5

What are the factors of the algebraic term 3x?

• 3 and 3x

• x and 3x

• 3 and x

• 1 and 3x

When factorising an expression, what should you take out?

• The smallest common factor

• The highest common factor

• Any random factor

• The sum of all factors

In the expression 3x + 15, what is the highest common factor?

• 3

• 1

• 15

• 5

After factorising 3x + 15 by taking out the highest common factor, what is the resulting expression?

• x + 15

• 3x + 5

• x + 5

• 3(x + 5)

What is the highest common factor in the expression 6ab - a^2b?

• a

• 6

• b

• ab

When factorising 6ab - a^2b, what is left inside the brackets after taking out the highest common factor?

• 6a - b

• 6 - ab

• 6 - a

• 6b - a

In the expression pqr, which letter is a common factor?

• r

• None

• q

• p

What is the factorisation of the expression 25p^2 - 10p?

• 5p(5p - 2)

• 5(5p - 2)

• 5p(p - 2)

• 25p(p - 2)