Question

Bài 2 phân tích đa thức thành nhân tử a) x^2 +y^2+2xy-25 b) x^2+2x-15 c) x^2-x-2 d) 3x^2 -11x+6

Answer 1

`#040911`

`a)`

`x^2 + y^2 + 2xy - 25`

`= (x^2 + 2xy + y^2) - 25`

`= [ (x)^2 + 2*x*y + (y)^2] - 5^2`

`= (x + y)^2 - 5^2`

`= (x + y - 5)(x + y + 5)`

`b)`

`x^2 + 2x - 15`

`= x^2 + 5x - 3x - 15`

`= (x^2 + 5x) - (3x + 15)`

`= x(x + 5) - 3(x + 5)`

`= (x - 3)(x + 5)`

`c)`

`x^2 - x - 2`

`= x^2 - 2x + x - 2`

`= (x^2 - 2x) + (x - 2)`

`= x(x - 2) + (x - 2)`

`= (x + 1)(x - 2)`

`d)`

`3x^2 - 11x + 6`

`= 3x^2 - 9x - 2x + 6`

`= (3x^2 - 9x) - (2x - 6)`

`= 3x(x - 3) - 2(x - 3)`

`= (3x - 2)(x - 3)`

Answer 2

`a, (x+y)^2-25 = (x+y+5)(x+y-5)`.

`b, x^2+2x-15 = (x+1)^2-16 = (x-3)(x+5)`.

`c, x^2-x-2=(x-2)(x+1)`

`d, 3x^2-11x+6 = (3x-2)(x-3)`.

Answer 3

\(a)x^2+y^2+2xy-25\\ =\left(x+y\right)^2-5^2\\ =\left(x+y+5\right)\left(x+y-5\right)\\ b)x^2+2x-15\\ =x^2+2x+1-16\\ =\left(x+1\right)^2-4^2\\ =\left(x+1+4\right)\left(x+1-4\right)\\ =\left(x+5\right)\left(x-3\right)\\ c)x^2-x-2\\ x^2+x-2x-2\\ =x\left(x+1\right)-2\left(x+1\right)\\ =\left(x+1\right)\left(x-2\right)\\ d)3x^2-11x+6\\ =3x^2-2x-9x+6\\ =x\left(3x-2\right)-3\left(3x-2\right)\\ =\left(x-3\right)\left(3x-2\right)\)