忽!! 數學題20題~20分!－rlz87tm45t的部落格

標題:

忽!! 數學題20題~20分!

發問:

factorize the following polynomials要步驟! THX!!1. 6X^2 +5X+12. 2Y62+5Y+23. -8X^2-2X+34. 6P^2-7P+15. 13U^2-136. 6M^2+13M+67. UV+U^2+V+U8. (3N+1)^2-(2U-7)^29. 40M^3N-135N^410. 6X^2+10X+411.-64+(12M-5)^212. -48H^2+12H+613. 3X^2-4814 3M^2-6MN-9N^215.18P^2+33PQ+14Q^216.... 顯示更多 factorize the following polynomials 要步驟! THX!! 1. 6X^2 +5X+1 2. 2Y62+5Y+2 3. -8X^2-2X+3 4. 6P^2-7P+1 5. 13U^2-13 6. 6M^2+13M+6 7. UV+U^2+V+U 8. (3N+1)^2-(2U-7)^2 9. 40M^3N-135N^4 10. 6X^2+10X+4 11.-64+(12M-5)^2 12. -48H^2+12H+6 13. 3X^2-48 14 3M^2-6MN-9N^2 15.18P^2+33PQ+14Q^2 16. 8U^2-38UV-33V^2 17.ABC-A^2B-C^2+AC 18. 32P^3+32P^2+8P 19. 216B4-A^3B 20. A^2-AC-AB+BC 更新: 打錯字:忽- 急

最佳解答:

factorize the following polynomials 1. 6X2 +5X+1 6x2 + 5x + 1 = (2x+1)(3x+1) ================================== 2. 2Y2+5Y+2 2Y2 + 5Y + 2 = (Y+2)(2Y+1) ================================== 3. -8X2-2X+3 -8X2 - 2X + 3 = -[8X2 + 2x - 3] = -(2X-1)(4X+3) ================================== 4. 6P2-7P+1 6P2 - 7P + 1 = (P-1)(6P-1) ================================== 5. 13U2-13 13U2 - 13 = 13(U2 - 12) = 13(U-1)(U+1) ....... as a2-b2=(a+b)(a-b) ================================== 6. 6M2+13M+6 6M2 + 13M + 6 = (2M+3)(3M+2) ================================== 7. UV+U2+V+U UV + U2 + V + U = U(V+U) + (V+U) = (U+1)(V+U) = (U+1)(U+V) ================================== 8. (3N+1)2-(2U-7)2 (3N+1)2 - (2U-7)2 = [(3N+1)-(2U-7)][(3N+1)+(2U-7)] ....... as a2-b2=(a+b)(a-b) = [3N+1-2U+7][3N+1+2U-7] = (3N-2U+8)(3N+2U-6) ================================== 9. 40M^3N-135N^4 40M3N - 135N^4 = 5N(8M3 - 27N3) = 5N[(2M)3 - (3N)3] = 5N(2M-3N)[(2M)2 + (2M)(3N) + (3N)2] ....... as a3-b3=(a-b)(a2+ab+b2) = 5N(2M-3N)(4M2 + 6MN + 9N2) ================================== 10. 6X2+10X+4 6X2 + 10X + 4 = 2(3X2 + 5X + 2) = 2(X+1)(3X+2) ================================== 11.-64+(12M-5)2 -64 + (12M-5)2 = (12M-5)2 - 64 = (12M-5)2 - 82 = [(12M-5)+8][(12M-5)-8] ....... as a2-b2=(a+b)(a-b) = (12M+3)(12M-13) = 3(4M+1)(12M-13) ================================== 12. -48H2+12H+6 -48H2 + 12H + 6 = -6(8H2 - 2H - 1) = -6(2H-1)(4H+1) ================================== 13. 3X2-48 3X2-48 = 3(X2 - 16) = 3(X2 - 42) = 3(X-4)(X+4) ....... as a2-b2=(a+b)(a-b) ================================== 14 3M2-6MN-9N2 3M2 - 6MN - 9N2 = 3(M2 - 2MN - 3N2) = 3(M-3N)(M+N) ================================== 15.18P2+33PQ+14Q2 18P2 + 33PQ + 14Q2 = (6P+7Q)(3P+2Q) ================================== 16. 8U2-38UV-33V2 8U2 - 38UV - 33V2 = (2U-11V)(4U+3V) ================================== 17.ABC-A2B-C2+AC ABC - A2B - C2 + AC = AB(C-A) - C(C-A) = (AB-C)(C-A) ================================== 18. 32P3+32P2+8P 32P3 + 32P2 + 8P = 8P(4P2 + 4P + 1) = 8P(2P+1)2 ================================== 19. 216B4-A^3B 216B^4 - A3B = B(216B3 - A3) = B[(6B)3 - A3] = B(6B-A)[(6B)2 + (6B)(A) + A2] ....... as a3-b3=(a-b)(a2+ab+b2) = B(6B-A)[36B2 + 6AB + A2] = B(6B-A)[A2 + 6AB + 36B2] ================================== 20. A2-AC-AB+BC A2 - AC - AB + BC = A(A-C) - B(A-C) = (A-B)(A-C) ================================== 2006-12-05 17:49:36 補充：小小補充：做 factorization 的時候，下面的恆等式可以幫到你：a2-b2 = (a+b)(a-b)(a+b)2 = a2+2ab+b2(a-b)2 = a2-2ab+b2只是不同的項代入 a 和 b。 2006-12-05 17:53:37 補充： ooo 下面的照 copy 我的答案 ... 連分隔線都一樣 >.