Đáp án:
Giải thích các bước giải:
$1) 2x^3+x^2+2x+1= (2x^3+2x)+(x^2+1)\\ = 2x(x^2+1)+(x^2+1)= (x^2+1)(2x+1)\\ 2) x^3-5x^2+4x-20= (x^3-5x^2)+(4x-20)\\ = x^2(x-5)+4(x-5)= (x-5)(x^2+4)\\ 3) 3x^4-x^3-6x+2= (3x^4-6x)-(x^3-2)\\ = 3x(x^3-2)-(x^3-2)= (x^3-2)(3x-1)\\ 4) x^3y+x^2y^2-4x-4y=(x^3y+x^2y^2)-(4x+4y)\\ = x^2y(x+y)-4(x+y)= (x+y)(x^2y-4)\\ 5) x^2-4y^2+3x+6y= (x^2-4y^2)+(3x+6y)\\ = (x-2y)(x+2y)+3(x+2y)= (x+2y)(x-2y-1)\\ 6) x^2-4xy+4y^2-81= (x^2-4xy+4y^2)-81\\ = (x-2y)^2-9^2= (x-2y-9)(x-2y+9)\\ 7) x^2-25+2xy+y^2= (x^2+2xy+y^2)-25\\ = (x+y)^2-5^2 = (x+y-5)(x+y+5)\\ 8) 15x+4-9x^2-10= (15x-10)-(9x^2-4)\\ = 5(3x-2)-(3x-2)(3x+2)= (3x-2)(5-3x-2)\\ 9) ax^2+ay-bx^2-by = (ax^2+ay)-(bx^2+by)\\ = a(x^2+y)-b(x^2+y)= (x^2+y)(a-b)$
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