F.3 Maths (Factorization) 10 點

1.) x³ +y³ +3x+3y= (x + y)(x² - xy + y²) + 3(x + y)= (x + y)(x² - xy + y² + 3)
2.) (3x-2)³ -8(x+1)³= (3x-2)³ - [2(x+1)]³= (3x-2 - (2x+2)) ((3x-2)² + (3x-2)(2x+2) + (2x+2)²)= (x - 4) (9x² - 12x + 4 + 6x² + 2x - 4 + 4x² + 8x + 4)= (x - 4) (19x² - 2x + 4)
3.a) x² +ax+96 = (x+b)(x-12) = x² + (b-12)x - 12bComparing coefficients :b - 12 = a ....(1)96 = - 12b ....(2)By (2) , b = - 8 , sub into (1) :a = - 8 - 12 = - 203b)(a+y)(y-b)+75= (y - 20)(y + 8) + 75= y² - 12y - 160 + 75= y² - 12y - 85= (y - 17)(y + 5)4a)(x+1)(x-6)-8= x² - 5x - 6 - 8= x² - 5x - 14= (x - 7)(x + 2)4b)(2y²+5y+1)(2y²+5y-6)-8Let x be 2y²+5y , sub into the result in a) part ,= (2y²+5y - 7)(2y²+5y + 2)= (2y + 7)(y - 1) (2y + 1)(y + 2)= (y - 1)(y + 2)(2y + 1)(2y + 7)