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To check this answer is correct, expand the bracket and check that the answer matches the original equation:

EXAMPLE 3 Factoring an Algebraic Expression Factor the expression using the GCF. The original expression shows a total savings of 15. To factorise 5a2 10awe simply reverse the process. If we expand the expression 5a(a 2) we obtain 5a2 10a. Put this outside the bracket:įind the missing terms in the bracket by dividing each term by the HCF: So, the factored expression shows a 3 discount for every book you buy. To factorise an algebraic expression, we must determine the highest common factor (HCF) of the terms and insert grouping symbols, usually parentheses. Find the missing terms in the brackets by dividing each of the terms given in the question by the HCF. The process of factoring is essential to the simplification of many algebraic expressions and is a useful tool in solving higher degree equations. To factorise, write down the HCF and then begin a set of brackets. If the terms have common factors, then factor out the greatest common factor (GCF) and look at the. (3) Always factor completely, which means to go back and try to factor factors even further. 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 this expression, look for the HCF of \(6x\) and 9 which is 3. General Factoring Strategy Check for common factors. When we are factoring numbers or factoring polynomials, we are finding. 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 polynomial expressions is not quite the same as factoring numbers. 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.