Factor a Perfect Square Trinomial High School Algebra Aligned to Common Core State Standards

1. Factor a Perfect Square Trinomial High School Algebra Aligned to Common Core State Standards

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3. Perfect Square Trinomials Perfect square trinomials are the result of squaring a binomial. (x + 9)2 = (x + 9)(x + 9) = x2 + 9x + 9x + 81 = x2 + 18x + 81 F O I L F = first, O = outside,I = inside, L = last In general terms (a + b)2 = a2+ ab+ ab+ b2= a2 + 2ab + b2 (a – b)2 = a2– ab–ab+ b2 = a2 – 2ab + b2

4. Expand the following. • (5t – 3)2 = • (w + 6)2 = • (2s – 7)2 = • (11x + 8)2 =

5. Expand the following. • (5t – 3)2 = 25t2 – 30t +9 • (w + 6)2 = w2 + 12w + 36 • (2s – 7)2 = 4s2 – 28s + 49 • (11x + 8)2 = 121x2 + 176x + 64

6. Factoring a Perfect Square Trinomial • In general terms • (a + b) 2= a2 + ab + ab + b2 = a2+ 2ab + b2 • (a – b) 2= a2 – ab – ab + b2 = a2– 2ab + b2 • Taking this in the reverse, you would factor a perfect square trinomial like this: • a2 + 2ab + b2 = (a + b)2 • a2 – 2ab + b2 = (a – b)2

7. Factoring Steps Factor 49x2+ 28 x + 4 (7x +2)2 Check the middle term by multiplying the first term and last term and doubling. [(7x)(2)]2 =28xThis matches the middle term and therefore is the correct factorization. Take the square root of the first term, the sign of the second term, and the square root of the third term. Square the quantity.

8. Factor the following. • m2 – 10m + 25 = • 144p2 – 24p + 1 = • 81n2 + 54n + 9 =

9. Factor the following. • m2 – 10m + 25 = (m – 5)2 • 144p2 – 24p + 1 = (12p – 1)2 • 81n2 + 54n + 9 = (9n + 3)2

10. Solve using the Zero Product Property. Use the reasons given for each step to guide you. x2 = 3(2x – 3)

11. Solve using the Zero Product Property. Use the reasons given for each step to guide you. x2 = 3(2x – 3) x2 = 6x – 9 x2 – 6x = - 9 x2– 6x + 9 = 0 (x – 3)2 = 0 x – 3 = 0 x – 3 = 0 x = 3 x = 3

12. Find the zeros of the function. 4x2 12x + 9 = 0

13. Solve and graph the solution. 25x2 + 4 = 20x

14. Solve and graph the solution. 25x2 + 4 = 20x 25x2 20x + 4 = 0 (5x  2)2 = 0 5x  2 = 0 5x  2 = 0 5x = 2 5x = 2 x = 2/5 x = 2/5 The graph will intersect the x-axis at (.4, 0). It will open up since the coefficient of x2 is positive. The axis of symmetry is x = –b/2a or x = –(-20)/2(25) = 20/50 = 2/5.

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