How do you factor the trinomial #30x²+x-1#?

1 Answer
George C.
Jan 24, 2016

Find a pair of factors of #30# that differ by #1#, namely #6# and #5#, hence:

#30x^2+x-1 = (6x-1)(5x+1)#

Explanation:

Ignoring signs, call the coefficients of this quadratic #A#, #B# and #C#.

Look for a pair of factors of #AC = 30*1 = 30# which differ by #B=1#.

The pair #6#, #5# works.

We can use this pair to split the middle term then factor by grouping as follows:

#30x^2+x-1#

#=30x^2+6x-5x-1#

#=(30x^2+6x)-(5x+1)#

#=6x(5x+1)-1(5x+1)#

#=(6x-1)(5x+1)#

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