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#1 2010-08-17 01:29:17

atut
Member
Registered: 2008-04-23
Posts: 30

Factorsing Quadratic Expressions

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

Factorise this Quadratic Expression:

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#2 2010-08-17 01:33:46

atut
Member
Registered: 2008-04-23
Posts: 30

Re: Factorsing Quadratic Expressions

11k^2 + 51k + 28

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#3 2010-08-17 01:52:24

Bob
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Registered: 2010-06-20
Posts: 10,627

Re: Factorsing Quadratic Expressions

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)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#4 2010-08-17 02:03:44

Bob
Administrator
Registered: 2010-06-20
Posts: 10,627

Re: Factorsing Quadratic Expressions

Whoops.

Corrected diagram below


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2010-08-17 02:08:14

Bob
Administrator
Registered: 2010-06-20
Posts: 10,627

Re: Factorsing Quadratic Expressions

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


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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