Factorise [tex]x^2-x[/tex]
Answer (2)
Identify the common factor x in both terms.
Factor out the common factor x from the expression.
The factorised form of the expression is x ( x − 1 ) .
Explanation
Understanding the problem We are asked to factorise the expression x 2 − x . This means we need to find the common factors in both terms and rewrite the expression as a product of these factors.
Factoring out the common factor Both terms in the expression, x 2 and − x , have x as a common factor. We can factor out x from both terms: x 2 − x = x ( x − 1 )
Final Answer Therefore, the factorised form of x 2 − x is x ( x − 1 ) .
Examples
Factoring is a fundamental skill in algebra and is used extensively in solving equations and simplifying expressions. For example, if you want to find the roots of the quadratic equation x 2 − x = 0 , you can factorise it as x ( x − 1 ) = 0 . This tells you that the solutions are x = 0 or x = 1 . Factoring also helps in simplifying complex algebraic expressions, making them easier to work with.
The expression x 2 − x can be factorised by identifying the common factor x , resulting in x ( x − 1 ) . This simplifies the expression and makes solving equations easier. The factorised form is essential for finding the roots of the equation, like in x ( x − 1 ) = 0 .
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