How do you factor #3b^2-13b+4#?

1 Answer
George C.
May 24, 2015

If #3b^2-13b+4 = 0# has a rational root #p/q# in lowest terms, then #p# is a divisor of the constant term #4# and #q# is a divisor of the coefficient #3# of the highest order term #3b^2#.

That means any rational root must be one of:

#+-1#, #+-1/3#, #+-2#, #+-2/3#, #+-4# or #+-4/3#

Notice that #4# is a root (try substituting #b=4# and find the result is #0#), so #(b-4)# is a factor of #3b^2-13b+4#.

That leaves #(3b-1)# as the other factor - check #1/3# is a root too - yes.

So #3b^2-13b+4 = (b-4)(3b-1)#

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