Factoring Perfect Square Trinomial
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The document discusses factoring perfect square trinomials (polynomials with three terms where the first and last terms are perfect squares). It provides examples of factoring expressions like x^2 + 8x + 16 into (x + 4)^2. For an expression to be a perfect square trinomial, the first term must be a perfect square, the third term must be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms. Students are provided examples and exercises to practice factoring various square trinomial expressions.
Factoring Perfect Square Trinomial
- 2. 1. (x + 4)2 2. (x + 5)2 = x2 + 8x + 16 = x2 + 10x + 25 3. (x + 7)2 = x2 + 14x + 49 4. (x - 9)2 = x2 - 18x + 81 5. (x - 11)2 = x2 - 22x + 121 Drill
- 3. The first criteria of a Perfect Square Trinomial is that it must have three terms. x2 + 8x + 16
- 4. The first term must be a perfect square x2 = ( x )( x ) x2 + 8x + 16
- 5. The third term must be a perfect square 16 = ( 4 )( 4 ) x2 + 8x + 16
- 6. The middle term must be twice the product of the square root coefficient of the first and last term. (2)(1)(4) = 8 x2 + 8x + 16
- 7. Perfect Square Trinomial 1. r2 – 8r + 16 YES 2. x2 – 14x + 49 3. d2 + 50d + 225 4. x2 + 2x + 1 5. b2 – 5b + 36 YES YES NO NO Yes or No?
- 8. WHAT IF IT IS A PERFECT SQUARE TRINOMIAL? If you have a perfect Square Trinomial it is easy to factor: •Take the square root of the first term. •Take the square root of the last term. •Use the sign of the middle term, put in parenthesis and square the result.
- 9. x2 + 4x + 4 x (x+2) 2 = (x+2) (x+2) x2 + 4x + 4 = (x+2) (x+2) Factors 2+ Example:
- 10. = x + 5( ) 2 x2 + 10x + 25 Another example:
- 11. 1. r2 – 8r + 16 Give the factors of the given examples. = ( r – 4 )2 2. x2 – 14x + 49 = ( x – 7 )2 4. x2 + 2x + 1 = ( x + 1)2
- 12. Board Exercises 1. y2 - 6y + 9 2. a2 + 12a + 36 3. m2 - 18m + 81 4. y2 - 16y + 64 5. b2 - 12b + 36 Factor the following square trinomials.
- 13. Factor completely each of the following expression. 1. x2 + 10x + 25 2. a2 - 8a + 16 3. 9x2 + 6xy + y2 4. x2 + 2x + 1 5. 169 + 26b + b2 Seatwork
- 14. 1. x2 – x + 1/4 2. 36m2 - 84m + 49 3. 4x2 - 12x + 9 4. p2 + 30p + 225 5. 64x2 - 176x + 121 Homework Factor completely each of the following expression.