Factorise fully the following:
a) $x^2+3 x$
Answer (1)
The expression x 2 + 3 x is factorised by identifying the common factor x in both terms. Factoring out x results in the expression x ( x + 3 ) . The fully factorised form of x 2 + 3 x is: x ( x + 3 ) .
Explanation
Understanding the Problem We are asked to factorise the expression x 2 + 3 x fully. This means we want to write it as a product of simpler expressions.
Identifying Common Factors We look for common factors in the terms x 2 and 3 x . Both terms have x as a factor. We can write x 2 = x ⋅ x and 3 x = 3 ⋅ x .
Factoring Out the Common Factor Now, we factor out the common factor x from the expression: x 2 + 3 x = x ( x + 3 ) .
Final Factorised Form The expression x + 3 cannot be factored further. Therefore, the fully factorised form of x 2 + 3 x is x ( x + 3 ) .
Examples
Factoring is a fundamental skill in algebra. For example, if you are designing a rectangular garden where the area is given by x 2 + 3 x square meters, you might want to know the possible dimensions of the garden. By factoring the expression to x ( x + 3 ) , you know that the width could be x meters and the length could be x + 3 meters. This helps in planning the layout and fencing of the garden.
