How do you factor $12p^2+16p+5$ ?

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Answer 1 · 2015-06-02T14:46:51

$(6p+5)(2p+1)$

Use the quadratic formula for solving $ax^2+bx+c=0$

$x=(-b+-sqrt(b^2-4ac))/(2a)$

Taking $b^2-4ac$ this is $16^2-4.12.5 = 256-240=16$ , $sqrt(16)=4$

This gives $p=(-16+-4)/(2.12)$ thus $p =-12/24 or -20/24$

Simplifying gives $p=-1/2 or p=-5/6$

These can be written as $2p+1=0 or 6p+5=0$

Hence $12p^2+16p+5=(6p+5)(2p+1)$

How do you factor 12p^2+16p+512p^2+16p+5?