Can the Polearm Master 1d4 bonus attack be used with Great Weapon Fighter/Master?

Question

Until recently, I've been thinking of the extra love tap from Polearm Master as basically no better than dual wielding a dagger, but now I found out that not only does it benefit from ability bonus to damage, but I saw people claiming that, since you're attacking with a two-handed weapon, you're entitled to the rerolls of Great Weapon Fighting

When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll, even if the new roll is a 1 or a 2. The weapon must have the Two-Handed or Versatile property for you to gain this benefit.

... or the ability to power attack of Great Weapon Master ...

Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack's damage.

And, bizzarely enough, I can't think of a reason these two wouldn't, since both the Halberd and the Glaive have the Two-handed and Heavy properties... Is this right?

Answer 1

This looks like it would work, RAW

The Polearm Master feat (PHB, pg. 168) states:

When you take the Attack action and attack with only a glaive, halberd, or quarterstaff, you can use a bonus action to make a melee attack with the opposite end of the weapon. This attack uses the same ability modifier as the primary weapon. The weapon's damage die for this attack is a d4, and the attack deals bludgeoning damage.

Great Weapon Fighting (PHB, pg. 72/84) states:

When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll, even if the new roll is a 1 or a 2. The weapon must have the Two-Handed or Versatile property for you to gain this benefit.

The Great Weapon Master feat (PHB, pg. 167) states:

Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack's damage.

As PJRZ points out, the GWM feat wouldn't work with a quarterstaff since it's not a Heavy weapon, but with a glaive or halberd, it would; the Great Weapon Fighting style would work will all three weapons (since all three are either Two-Handed or Versatile).

You are making a melee attack with a Heavy weapon, so you could potentially add +10 to that d4+STR! And, you are making a melee attack with a Two-Handed weapon that you are wielding with two hands, so you could also reroll 1s or 2s on the d4!

Answer 2

The glaive and halberd are both two-handed weapons and heavy weapons. So they would qualify for both the Great Weapon Fighting and Great Weapon Master features in addition to Polearm Master

The quarterstaff has the 'Versatile' property, meaning it can be used with one or two hands.

This would qualify it for the reroll feature of Great Weapon Fighting that says "The weapon must have the Two-Handed or Versatile" property.

However, it is not a heavy weapon, so would not qualify it for the power attack feature of Great Weapon Master (compare to the Glaive that specifically has the "heavy" property).