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Factorising Quadratics – The Box Method AS Maths

Before we factorise quadratics, we must… Ensure that the problem is in standard form. (This means the highest exponents must come first!) Factorise by greatest common factor (if any exists) Example: Ensure that the leading coefficient is positive!

Review Factorise the following: (a) (e) (b) (f) (c) (g) (d) (h)

Solutions (a) (e) (b) (f) (c) (g) (d) (h)

Factorising when a>1 Factorising quadratics that have a leading coefficient greater than 1 isn’t quite so simple. There are many methods for factorising these type problems such as: Trial and error “Bust the B” (multiply a & c) Fancois Viete The Box Method this is the method we’ll use today!

Factorising using the box method Step 1: Put in standard form & FACTORISE by GCF!!!! Step 2: Put the 1st term in the 1st box, and last term in the last box. Step 3: Multiply those terms together & write the solution in the margin of your paper. Step 4: Find two numbers that MULTIPLY to give you the solution to step 3, but ADD to give you the middle term. Write these chosen factors in the empty boxes. Step 5: Factorise every row and column by GCF, putting your answer on the outside of the box. The sign of the answer follows the sign of the box it’s closest to. Step 6: Your answer is lying on the outside of the boxes. Rewrite in factorised form. ( )( ) NOTE TO SELF: NEXT YEAR PRINT THESE STEPS FOR STUDENTS TO GLUE IN BOOK!

Example 1 Final answer = Factorise Which pair adds to get the middle term? Find the Greatest Common Factor! Final answer =

Example 2 Final answer = Factorise Find the Greatest Common Factor! Which pair adds to get the middle term?

Example 3 Final answer = Factorise Notice: this quadratic has a common factor! Factor by GCF first! Example 3 Factorise We only use the box method on the inside polynomial! Find the Greatest Common Factor! Which pair adds to get the middle term? Final answer = Don’t forget to include our first factor!

Difference of two squares A difference of two squares comes in the form of a binomial (meaning it has two terms). Looks like: To factorise – take the square root of each term and place in brackets in the following form: x is a perfect square c is a perfect square MUST be subtraction always a + always a –

Example 4 Factorise completely. (a) (d) (b) (e) (c) (f)

Hint… NOT FACTORABLE Factorise by GCF There are only 2 ways to factorise a binomial (a polynomial with 2 terms) Factorise by GCF Factorise by difference of two squares Therefore, if neither of those options work, it is NOT FACTORABLE

Independent Study: Complete the mymaths online assignment over: Factorising Quadratics Copy & complete each question notebook, show all work, and mark in a colourful pen. DUE NEXT LESSON.