07B2-factorising-quads

= Factorising Quadratics when a equals 1 =

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

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


 * Shortcut a = 1 **

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Method

 * 1) Take the last term (the constant) and list pairs of factors for that value
 * 2) Look for a pair in your list that combine (add or subtract) to give the middle term (the coefficient of x)
 * 3) If the last term is positive, use ** + + ** or ** – – **
 * 4) If the last term is negative, use ** + – ** or ** – + **
 * 5) Write the double brackets, put x at the front of each bracket
 * 6) Put the pair you found in step 2 into the brackets (one in each) . Include the signs.


 * Advanced Quadratics **


 * Example **

math . \qquad \text{Factorise : } \big( x + 3 \big)^2 - 2\big( x + 3 \big) - 15 math


 * Solution:**

... ... Recognise that the same term appears in both brackets. ... ... Replace that term in the brackets with a new pronumeral

... ... //Let u = x + 3 //

math \\ . \qquad u^2 - 2u - 15 \qquad \qquad \{ \textit{now factorise} \} \\. \\ . \qquad = \big( u - 5 \big) \big( u + 3 \big) \qquad \qquad \{ \textit{now replace u with (x + 3)} \} \\. \\ . \qquad = \big( x + 3 - 5 \big)\big( x + 3 + 5 \big) \quad \qquad \{ \textit{simplify inside each bracket} \} \\.\\ . \qquad = \big( x - 2 \big) \big( x + 8 \big) math

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