6.3 Trinomial Squares Goals: To recognize a trinomial square and be able to factor it Remember to always factor out a common factor before you see if it is a trinomial square or not!!
Checklist to see if it is a Trinomial Square Are the first and last terms perfect squares? Are the first and last terms positive? Is the middle term the product of the first two term’s square root multiplied by 2?
Song Sung to the "itsy bitsy spider" First you take the square root of terms one and three. Double the product, then you check to see, If it matches term two you're ready to declare The three-term trinomial is a perfect square.
Trinomial Squares 4x2 – 20x + 25 4x² and 25 are perfect squares 4x² and 25 are positive The square root of 4x² is 2x and the square root of 25 is 5. Thus (2x) (5) is 10x then multiply it by 2 and we get 20x which is the middle term!
Is x2 + 8x + 16 a Trinomial Square? Yes!! Are the first and last terms perfect squares? Are the first and last terms positive? Is the middle term the product of the first two term’s square root multiplied by 2?
Is x2 - 12x + 4 a Trinomial Square? Are the first and last terms perfect squares? Are the first and last terms positive? Is the middle term the product of the first two term’s square root multiplied by 2?
Is 9x2 - 12x + 16 a Trinomial Square? Are the first and last terms perfect squares? Are the first and last terms positive? Is the middle term the product of the first two term’s square root multiplied by 2?
To Factor Trinomial Squares: A2 + 2AB + B2 (A + B)2 A2 - 2AB + B2 (A - B)2 Factor: x2 + 10x + 25 (x + 5)2
To Factor Trinomial Squares: A2 + 2AB + B2 (A + B)2 A2 - 2AB + B2 (A - B)2 Factor: x2 - 8x + 16 (x - 4)2
To Factor Trinomial Squares: A2 + 2AB + B2 (A + B)2 A2 - 2AB + B2 (A - B)2 Factor: 4x2 + 12x + 9 (2x + 3)2
To Factor Trinomial Squares: A2 + 2AB + B2 (A + B)2 A2 - 2AB + B2 (A - B)2 Factor: 2x2 + 12x + 18 2(x2 + 6x + 9) 2(x + 3)2
Factor: x2 - 8x + 16 ( - )2 x 4 (x – 4)(x – 4) ( - )2 x 4 Check your answer using FOIL or put it in a chart (x – 4)(x – 4)
Factor: 4x2 + 12x + 9 (2x + 3)2
Factor: 9x2 + 30xy + 25y2 (3x + 5y)2
Factor: 2x2 + 12x + 18 2(x2 + 6x + 9) 2(x + 3)2
Assignment: Page 271 4-30 even