07b3-factorising-quads

= Factorising Quadratics with a not equal to 1 =

Recall that a quadratic has the form : ** a x 2 + b x + c **
 * where ** a, b, c ** are real numbers

Today, we factorise a quadratic where a ≠ 1 (a is the coefficient of x 2 )

Full Method a ** ≠ ** 1


To see the process step by step, click on these links media type="custom" key="21764268" media type="custom" key="21764274" ... media type="custom" key="21764276" ... media type="custom" key="21764278" ... media type="custom" key="21764280" media type="custom" key="21764282" ... media type="custom" key="21764284" ... media type="custom" key="21764286"

media type="custom" key="21764410" ... media type="custom" key="21764412" ... media type="custom" key="21764414" ... media type="custom" key="21764420" media type="custom" key="21764422" ... media type="custom" key="21764430" ... media type="custom" key="21764436"

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Method

 * 1) Multiply the first and the last term (a × c) and list pairs of factors for that product
 * 2) Look for a pair in your list that combine (add or subtract) to give the middle term of the quadratic (the coefficient of x)
 * 3) If the last term is positive, use ** + + ** or ** – – **
 * 4) If the last term is negative, use ** + – ** or ** – + **
 * 5) Split the middle term into two, using the pair of factors that you chose (including signs).
 * 6) You now have 4 terms -- factorise the first two terms and factorise the last two terms
 * 7) The brackets should now be the same (if they aren't then check your factorising)
 * 8) Take out the bracket as a common factor. (The result is the factorised quadratic)

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