【高校数学I】数と式を完全攻略～基本から応用までを徹底解説します！～因数分解-問題35

問題

次の式を因数分解せよ.

解説

• (1) $x^2+(3y+1)x+(y+4)(2y-3)$
  • $=$$(x+y+4)(x+2y-3)$
• (2) $x^2+3xy+2y^2-6x-11y+5$
  • $=x^2+(3y-6)x+2y^2-11y+5$
    $=x^2+(3y-6)x+(y-5)(2y-1)$
    $=$$(x+y-5)(x+2y-1)$
• (3) $x^2-2xy+y^2-x+y-2$
  • $=x^2-(2y+1)x+y^2+y-2$
    $=x^2-(2y+1)x+(y+2)(y-1)$
    $=$$(x-y-2)(x-y+1)$
• (4) $2x^2+5xy+2y^2+4x-y-6$
  • $=2x^2+(5y+4)x+2y^2-y-6$
    $=2x^2+(5y+4)x+(y-2)(2y+3)$
    $=$$(2x+y-2)(x+2y+3)$
• (5) $2x^2+xy-y^2+7x-5y-4$
  • $=2x^2+(y+7)x-(y^2+5y+4)$
    $=2x^2+(y+7)x-(y+1)(y+4)$
    $=$$(2x-y-1)(x+y+4)$
• (6) $2x^2+5xy-3y^2-x+11y-6$
  • $=2x^2+(5y-1)x-(3y^2-11y+6)$
    $=2x^2+(5y-1)x-(y-3)(3y-2)$
    $=$$(2x-y+3)(x+3y-2)$