- (x + 4)2
- (x + 5)2
- (3x + 2)2
The third rule to factoring is to look for perfect squares with three terms. A perfect square trinomial has the first term squared, the last term squared, and the middle is the square root of the first term times the square root of the second term times two.
Rule #3 If a polynomial has three terms and the first term is a square, the last term is a square and the middle term is two times the square root of the first and the last term, then it is a perfect square. There are two forms: one with a positive middle term and one with a negative middle term. |
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| ax2 + 2√a√cx + c = (√ax + √c)(√ax + √c) = (√ax + √c)2 |
Example 1: x2 + 6x + 9 (notice 9 is a perfect square)
= (x + 3)(x + 3) = (x + 3)2 |
| or | |
| ax2 -2√a√cx + c = (√ax - √c)(√ax - √c) = (√ax - √c)2 |
Example 2: 4x2 - 20x + 25 (notice 4 and 25 are perfect squares) = (2x - 5)(2x - 5) = (2x - 5)2 |
Look at these polynomials and decide if they are perfect square trinomials. If they are perfect square trinomials, factor them. Interactive popup. Assistance may be required.
All of these are perfect square trinomials.