Factorsing Quadratic Expressions

atut · 2010-08-17 01:29:17

I really do not understand how to get the 51k!!
The question is:

Factorise this Quadratic Expression:

atut · 2010-08-17 01:33:46

11k^2 + 51k + 28

Bob · 2010-08-17 01:52:24

Hi atut,

I start by looking for factors of 11 (only 11 x 1) and 28 (= 28 x 1 = 14 x 2 = 7 x 4 )

Any of those might be the factorisation so I do a quick check like this:

[ I'm picking one x term to go with one non-x term]

11 x 28 + / - 1 x 1 no good
11 x 1 + / - 1 x 28 also no good

11 x 14 + / - 1 x 2 .........
11 x 2 + / - 1 x 14 ...............

11 x 7 + / - 1 x 4 ...............

but
11 x 4 + 1 x 7 = 51

so (11x +7)(1x + 4)

Here's another example.

2x^2 - 7x -30

I've got to try 2 x 1 as the x terms and lots of ways to make 30 (30x1=15x2=10x3=5x6)

In other words I'm trying things like (2x -15)(x +2) and (2x + 10)(x - 3)

2 30 2 15 2 10 2 5
1 1 1 2 1 3 1 6

Out of all these I notice that 2 x 6 - 1 x 5 = 7 so that's the one I want.

(2x 5)(x 6)

Now sort out the signs. One must be a minus and I want -7x so

(2x + 5)(x - 6) = 2x^2 - 12x + 5x -30 = 2x^2 -7x -30

The diagram might help.

Last edited by Bob (2010-08-17 02:00:39)

Bob · 2010-08-17 02:03:44

Whoops.

Corrected diagram below

Bob · 2010-08-17 02:08:14

See also http://www.bundy.demon.co.uk/Lessons/LessonIndex.htm choose 'quadratic expressions'

I did this page a while ago. I think the book references are to Heinemann Intermediate GCSE Mathematics but I've lent the book so cannot check now.

Bob

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