How do you factor #5x^4+31x^2+6#?

1 Answer
Mar 16, 2017

Answer:

#5x^4 +31x^2 +6#

#=(5x^2 +1)(x^2 +6)#

Explanation:

#5x^4 +31x^2 +6#

Find factors of #5 and 6# whose products add to #31#

We can see that the largest product that we can find using #5 and 6# is 30, so we will not use smaller factors of #6#

#color(white)(.......)5 and 6#
#color(white)(......)darr" "darr#
#color(white)(.......)5" " 1" "rarr 1 xx1 = 1#
#color(white)(.......)1 " "6" "rarr 5 xx 6 = ul30#
#color(white)(...............................................)31#

The top row is the first bracket and the bottom row is the second bracket. The signs are all positive.

#5x^4 +31x^2 +6#

#=(5x^2 +1)(x^2 +6)#