How do you factor the trinomial #8b^2+2b-3#?

1 Answer
Nov 24, 2015

#(2b-1)(4b+3)#

Explanation:

Only factors of 3 are {1,3} so this is fixed giving the format of:

#(?+1)(?+3)#.......ignoring the signs

But we have a negative 3 so the signs for the factors need to opposites. One positive and the other negative!

Consider the factors of 8 #-> {1,8}, {2,4}#

So can we end up with 2 in 2b using these?

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#color(blue)("Attempt" color(white)(.) 1)#

#color(brown)((2b+1)(4b-3)color(blue)( = 8b^2 -6b+4b-3) =8b^2-2b-3) color(green)(" Fail")#

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#color(blue)("Attempt" color(white)(.) 2)#

In attempt 1 the 2 in #2b# is negative so we have the correct number but the sign is wrong. Try reversing the signs in the brackets.

#color(brown)((2b-1)(4b+3)color(blue)( = 8b^2-4b+6b-3))#

# color(brown)(=8b^2+2b-3) color(green)(" It works!")#

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