I recently changed jobs and my company paid me for the pension money that I had invested. The company deducted the federal taxes from the total amount, but my question is if I cash the check instead of reinvesting it, do I pay penalties?

That was your money. Why didn't they suggest a trustee to trustee transfer? Why wasn't it just rolled over and no taxes taken out. Was this a 401K? Depending on age you may pay penalties.

Yes, you will owe a 10% penalty of the total amount of distribution - i.e. the pre-tax amount, not the amount of the check - unless you are at least 55 years old. Better to put the money into an IRA - that way no taxes are owed (you'll get a refund) and no penalty. However - you must do this within 60 days of the account at your old company being closed, and you must fund the new IRA with an amount equal to the amount of your old account - in other words you must come up with the 20% that they deducted and put it together with the amount of the check fund your new IRA. This is why it is highly recommended that whenever changing jobs doing a direct rollover from the old employer's plan to an IRA or your new employer's plan rather than simply closing out the old account and receiving a check.