Could you please help me factorise this expression:
$\displaystyle 4x^2+2x-20$
Well there are many different ways to do this, but here is one...
For any quadratic $\displaystyle ax^2+bx+c$ multiply a and c together to get
$\displaystyle a\cdot c =4\cdot (-20)=-80$
Now we need to find factors of the above that add up to b
$\displaystyle b=2$ and note that $\displaystyle -8 \cdot 10=-80 \mbox{ and }-8+10=2$
So now we rewrite the b term as the sum above i.e
$\displaystyle 2x=-8x+10x$ to get
$\displaystyle 4x^2-8x+10x-20$ now group the first and last two terms to get
$\displaystyle 4x^2-8x+10x-20 \iff (4x^2-8x)+(10x-20)$
Now factor each grouping
$\displaystyle 4x(x-2)+10(x-2) = (x-2)(4x+10)=2(x-2)(2x+5)$
Interesting... this is the same question as in
http://www.mathhelpforum.com/math-he...rise-help.html
And both of the original posters are from the same country. Coincidence?
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