Factor completely over the set of polynomials with integer coefficients: 4(x+5)(x+6)(x+10)(x+12)−3x2.
Lets start by multiplying it all out.
4(x+5)(x+6)(x+10)(x+12)−3x2=4(x4+[5+6+10+12]x3+[5∗6+5∗10+5∗12+6∗10+6∗12+10∗12]x2+[5∗6∗10+5∗6∗12+5∗10∗12+6∗10∗12]x+[5∗6∗10∗12](Sorry it's so long, I wanted to be complete.)
That simplifies to the more manageable, 4(x4+33x3+200x2+1980x+3600)−3x2=4x4+132x3+800x2−3x2+7920x+14400=4x4+132x3+797x2+7920x+14400
As for factoring it... you need to use a calculator (maybe this one?) Let's see how:
solve(4x^4+132x^3+797x^2+7920x+14400=0) = {x=-((sqrt(33*sqrt(193)+(901/4))/2))-((sqrt(193)/2))-((33/4)), x=(sqrt(33*sqrt(193)+(901/4))/2)-((sqrt(193)/2))-((33/4)), x=(sqrt(193)/2)-((sqrt((901/4)-(33*sqrt(193)))/2))-((33/4)), x=(sqrt(193)/2)+(sqrt((901/4)-(33*sqrt(193)))/2)-((33/4))}
That's your answer if you want the roots, but honestly, I doubt whoever gave you this problem was looking for this sort of answer (at least, I hope not )
Hope this helped!