How do you factor quadratics using grouping?
An example would be :4x^2-9x+5=0
I'm having difficulty understand this concept and would appreciate your help

Question

How do you factor quadratics using grouping? 
An example would be :4x^2-9x+5=0 
I'm having difficulty understand this concept and would appreciate your help

hartnn · Answer

@ww2greatbritainuk Hi,
$\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} $

amistre64 · Answer

consider 2 factors:

(x+a)(x+b)  when we multiply them together ... use your favorite method.  we get:

x^2 + ax + bx + ab , which simplifies to

x^2 + (a+b)x + ab

amistre64 · Answer

the idea with grouping is to try to split the middle (a+b) term into a sum of the factors of the last term (ab)

anonymous · Answer

So 5/4 and 1?

anonymous · Answer

(4x^2-4x)(-5x+5)
4x(x-1)-5(x-1)=0
(4x-5)(x-1)=0
x=5/4 x= 1

amistre64 · Answer

i was never great at grouping an usually go a different route to factor

:4x^2-9x+5=0 

4(5) = 20,  last term is + so factors are same sign

middle term is -, so factors are both negative

20 = 5*4,  and 5+4 = 9

therefore (x-5/4) (x-4/4) fit my idea, reduce and move denominators back in front

(4x-5) (x-1)

anonymous · Answer

Thanks!

amistre64 · Answer

youre welcome :)