01Zfactorisingquads

toc = Factorising Quadratics =

For a powerpoint explaining this process, download this file (3.1 Mbyte)

** Example 1 **
{Full process, coefficient of x 2 is 1}

Factorise x 2 + 5x – 14

{Take the last value (constant term) to the side (ignore sign for now) and list all the pairs of factors}

{Look for one pair of factors from the list that add or subtract to give the middle term (coefficient of x) In this case, +5} + 5 = – 2 + 7 {Check: –2 times +7 = –14 (matches sign of constant term)}

{Split the middle term into two parts using the pair of factors (and their signs) we have just identified} x 2 + 5x – 14 = x 2 – 2x + 7x – 14

{Separate the quadratic into 2 pairs and take out the common factor} = x 2 – 2x + 7x – 14 = x(x – 2) + 7(x – 2)

{Contents of the brackets should be identical. Take out the bracket as a common factor} = (x – 2)(x + 7)

{Done – check by expanding}

** Example 2 **
{short cut, coefficient of x 2 is 1}

Factorise x 2 – 9x + 20

{Take the last value (constant term) to the side and list all the pairs of factors (ignore sign for now)}

{Look for one pair of factors from the list that add or subtract to give the middle term (coefficient of x) In this case, –9} – 9 = – 4 – 5 {Check: –4 times –5 = +20 (matches sign of constant term)}

{Write the double brackets with the variable (x) in the first position of each bracket and the factors (with their signs) we have just identified in the second positions} x 2 – 9x + 20 = (x – 4)(x – 5)

{Done – check by expanding}

** Example 3 **
{full process, coefficient of x 2 is not 1}

Factorise 3x 2 – 4x – 4

{Take the first value (coefficient of x 2 ) and multiply by the last value (constant term). Write the product to the side (ignore sign for now) and list all the pairs of factors}

{Look for one pair of factors from the list that add or subtract to give the middle term (coefficient of x) In this case, –4} – 4 = + 2 – 6 {Check: +2 times –6 = –12 (product of x 2 coeff and constant term)}

{Split the middle term into two parts using the pair of factors (and their signs) we have just identified} 3x 2 – 4x – 4 = 3x 2 + 2x – 6x – 4

{Separate the quadratic into 2 pairs and take out the common factor} = 3x 2 + 2x – 6x – 4 = x(3x + 2) – 2(3x + 2)

{Contents of the brackets should be identical. Take out the bracket as a common factor} = (3x + 2)(x – 2)

{Done – check by expanding}

For another site that explains this idea, go here: MathsIsFun

** Example 4 **
{factorising on the CAS calculator}

In the MAIN screen, Select __**factor**__ from the ACTION menu, TRANSFORMATION submenu. Then type in the quadratic to be factorised and press EXE.

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