If we expand the expression 5a(a 2) we obtain 5a2 10a. Next look for factors that are common to all terms, and search out the greatest of these.
3x is the greatest common factor of all three terms.
To factor an expression by removing common factors proceed as in example 1. Each term of 10x + 5 has 5 as a factor, and 10x + 5 5 (2x + 1). To check this answer is correct, expand the bracket and check that the answer matches the original equation: To factorise an algebraic expression, we must determine the highest common factor (HCF) of the terms and insert grouping symbols, usually parentheses. In general, factoring will 'undo' multiplication. Put this outside the bracket:įind the missing terms in the bracket by dividing each term by the HCF: Find the missing terms in the brackets by dividing each of the terms given in the question by the HCF. EXAMPLE 3 Factoring an Algebraic Expression Factor the expression using the GCF. The original expression shows a total savings of 15. To factorise, write down the HCF and then begin a set of brackets. So, the factored expression shows a 3 discount for every book you buy. To factorise this expression, look for the HCF of \(6x\) and 9 which is 3. Factoring PolynomialsAlgebraFactoring PolynomialsGreatest Common FactorsFactoring by GroupingSpecial Factoring PatternsFactoring Trinomials Using Their. For example, \(2x\) is the HCF of \(4x^2\) and \(6x\) as 2 is the biggest number that will divide into 4 and 6 and \(x\) is the biggest variable that will divide into \(x^2\) and \(x\). Factoring (called Factorising in the UK) is the process of finding the factors: Factoring: Finding what to multiply together to get an expression. To factorise an expression fully, take out the highest common factor (HCF) of all the terms. A factorised answer will always contain a set of brackets. Factorising is the reverse process of expanding brackets.
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