Math Is Fun Forum

3dhomejoe

Member

Registered: 2006-02-09

Posts: 22

Perfect square trinomials

I have been home sick, and i got the hw for math but i dont know how to do it.

"Determine whether each trinomial is a perfect square trinomial. If so factor it."

1. c² - 6c + 9

(That is C squared subtract six C plus nine)

thanks

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3ddhomejoe

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Perfect square trinomials

A perfect square is something of the form (ax+b)². Your trinomial is monic (ie. there's no coefficient in front of the x²), so its perfect square form (if it had one) would be (x+b)², for some b.

The expanded form of this is x² + 2bx + b². By equating the x coefficients, you get 2b = -6. This implies that b = -3.

Now you check to make sure the constants match up. If they do then it's a perfect square trinomial, if they don't then it's not. (-3)² = 9, and so it's a match.

Therefore, x² - 6x + 9 is a perfect square trinomial and factoring it gives (x-3)².

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Why did the vector cross the road?
It wanted to be normal.