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Factor Difference of Squares 8-5 page 109, # 1 x 2 – 81 When the last term is negative, what are the signs? Both positive? Both negative? Mixed? (+)(+) (-)(-) (+)(-)

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8-5 page 109, # 1 Difference of two squares x 2 – 81 The last term is negative, so the signs are mixed. Mult to 81; subtracts to 0. (x+9)(x-9)

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8-5 page 109, # 1 Difference of two squares x 2 – 81 Easier Way Make signs mixed Square Root each term (x+9)(x-9)

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8-5 page 109, # 1 Difference of two squares x 2 + 81 Cannot factor. has + (sum) If it had a minus, it would factor.

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8-5 page 109, # 4 Difference of two squares 36x 2 – 100y 2 GCF: 4 Make signs mixed Square Root each term 4(9x 2 – 25y 2 ) 4(3x+5y)(3x-5y)

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8-5 page 109, # 12 Difference of two squares 8y 2 – 200 GCF:8 8(y 2 – 25) Mixed signs; square roots 8(y+5)(y-5)

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8-5 page 109, # 10 Difference of two squares - 81 + a 4 GCF: none Flip around a 4 – 81 Mixed signs; square roots (a 2 +9)(a 2 -9) factors more (a 2 + 9)(a + 3)(a – 3)

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Factor Trinomials 8-5 page 109, # 21 3x 4 + 6x 3 – 3x 2 – 6x GCF:3x x 3 + 2x 2 – x – 2 = 0 Group them (x 3 + 2x 2 )+(– x – 2) = 0 x 2 (x + 2) – 1(x + 2) = 0 (x 2 – 1) (x + 2) = 0

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Factor Trinomials 8-5 page 110, # 1 81x 2 = 49 set equal to 0 81x 2 - 49 = 0 Difference of two Squares (9x + 7)(9x – 7) = 0

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Factor Trinomials 8-5 page 110, # 4 1x 2 = 25 set equal to zero 4 1x 2 – 25 = 0 4 Next mult by denominator

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Factor Trinomials 8-5 page 110, # 4 1x 2 – 25 = 0 set equal to 0 4 mult by denominator x 2 – 100 = 0 (x + 10)(x – 10) = 0

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Factor Trinomials 8-5 page 111, # 1 x 2 – 16x + 64 Same Signs: both negative. (x – 8) (x – 8) (x – 8) 2

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Factor Trinomials 8-5 page 111, # 2 m 2 + 10m + 25 Same Signs: both positive. (m + 5) (m + 5) (m + 5) 2

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Factor Trinomials Prime: cannot factor x 2 + 10x + 3 Same Signs: both positive. But what mult to 3; adds to 10? Nothing 1 times 3 = 3 but 1 + 3 = 4 Prime; does not factor

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Prime Trinomials Not everything factors x 2 + nx + 8 8 x 1; 8+1; 4 x 2; 4 + 2; Only factors if middle term is 9 or 6. x 2 + 9x + 8 = (x + 8)(x + 1) x 2 + 6x + 8 = (x + 4)(x + 2) x 2 + 3x + 8 = Does not factor (Prime)

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