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標題:

F.2 Factorize

發問:

Factorize 1. 3x2-2(x-1) 2. (3t-1)(4t+5)+5(t+2) 3. 15(z+3)2+13(z+3)-2 4. 2x2+9xyz+4y2z2 5. x4-8x2-9 更新: myisland8132 ( 知識長 ) Please help me!!!

最佳解答:

您好，我是 lop，高興能解答您的問題。 (1) 3x2- 2(x-1) = 3x2- 2x + 2 Can not be factorzied (2) (3t-1)(4t+5) + 5(t+2) = 3t(4t+5) - (4t+5) + 5t + 10 = 12t2+ 15t - 4t - 5 + 5t + 10 = 12t2+ 16t + 5 = ( 12t2+ 10t ) + ( 6t + 5 ) = 2t(6t+5) + 1(6t+5) = (2t+1)(6t+5) (3) 15(z+3)2+ 13(z+3) - 2 = [ 15(z+3)2+ 15(z+3) ] - [ 2(z+3) + 2 ] = 15(z+3)[(z+3)+1] - 2[(z+3)+1] = [15(z+3)-2][(z+3)+1] = (15z+45-2)(z+3+1) = (15z+43)(z+4) (4) 2x2+ 9xyz + 4y2z2 = ( 2x2+ 8xyz ) + ( xyz + 4y2z2) = 2x(x+4yz) + yz(x+4yz) = (2x+yz)(x+4yz) (5) x?- 8x2- 9 = ( x?- 9x2) + ( x2- 9 ) = x2(x2- 9) + 1(x2- 9) = (x2+1)(x2-9) = (x2+1)(x2-32) = (x2+1)(x+3)(x-3)

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1. 3x2-2(x-1) =3x^2-2+2 2 (3t-1)(4t+5)+5(t+2) =15t^2+15t-4t+5+5t+10 =12t^2+16t+5 =(6t+5)(2t+1) 3. 15(z+3)2+13(z+3)-2 =[15(z+3)-2][(z+3)+1] =(15z+15+2)(z+1+1) =(15z+17)(z+2) 4. 2x2+9xyz+4y2z2 =(2x+yz)(x+4yz) 5. x4-8x2-9 =(x^2-9)(x^2+1) =(x-3)(x+3)(x^2+1)|||||15(z+3)2+13(z+3)-2 / 15(z+3)2+13(z+3)2