MAT 104 Quiz 14
Monday, October 18, 2004
1. Factor out the greatest common factor from
12x2
−2x+ 8
The gcd of the terms is 2, so this expression can be written as
2(6x2
−x+ 4)
2. Factor out the greatest common factor from
3x4y+ 9x3y2+ 12x2y2
The gcd of the terms is 3x2y, so this expression can be written as
3x2y(x2+ 3xy + 4y)
3. Factor by grouping
2z3+ 3z2
−6z−9
Group the first two terms together, and the last two terms together, and
pull out the gcd of each pair.
2z3+ 3z2
−6z−9 = (2z3+ 3z2)+(−6z−9)
=z2(2z+ 3) −3(2z+ 3)
Now we have a two term expression where the first term is z2(2z+ 3)
and the second term is −3(2z+ 3). They both have a common factor of
(2z+ 3), which can be pulled out. So
z2(2z+ 3) −3(2z+ 3) = (2z+ 3)(z2
−3)