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a) Hình như phân tích không được
b) \(2x^4+5x^3+13x^2+25x+15\)
\(=x^3+1+2x^4+2x^3+13x^2+13x+12x+12+2+2x^3\)
\(=\left(x^3+1\right)+\left(2x^4+2x^3\right)+\left(13x^2+13x\right)+\left(12x+12\right)+2\left(1+x^3\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x^3\left(x+1\right)+13x\left(x+1\right)+12\left(x+1\right)+2\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1+2x^3+13x+12+2x^2-2x+2\right)\)
\(=\left(x+1\right)\left(3x^2+10x+15+2x^3\right)\)
\(=\left(x+1\right)\left[x^2\left(2x+3\right)+5\left(2x+3\right)\right]\)
\(=\left(x+1\right)\left(x^2+5\right)\left(2x+3\right)\)
cái này cách tốt nhất là vào Cốc Cốc Math rồi gõ các nhân tử vào là nó sẽ ra nhé !
^_^
\(2x^4-9x^3+2x^3-9x^2+7x^2+7x+6x+6\)
\(\left(2x^4+2x^3\right)-\left(9x^3+9x^2\right)+\left(7x^2+7x\right)+\left(6x+6\right)\)
\(2x^3\left(x+1\right)-9x^2\left(x+1\right)+7x\left(x+1\right)+6\left(x+1\right)\)
\(\left(x+1\right)\left(2x^3-9x^2+7x+6\right)\)
b)\(\left(10x^4-50x^3y\right)+\left(23x^3y-115x^2y^2\right)+\left(5x^2y^2-25xy^3\right)-\left(2xy^3-10y^4\right)\)
\(10x^3\left(x-5y\right)+23x^2y\left(x-5y\right)+5xy^2\left(x-5y\right)-2y^3\left(x-5\right)\)
a)\(3x^2-8x+4\)
\(=3x^2-2x-6x+4\)
\(=x\left(3x-2\right)-2\left(3x-2\right)\)
\(=\left(x-2\right)\left(3x-2\right)\)
b)\(4x^4+81\)
\(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
c)\(x^8+98x^4+1\)
\(=\left(x^8+2x^4+1\right)+96x^4\)
\(=\left(x^4+1\right)^2+16x^2\left(x^4+1\right)+64x^4-16x^2\left(x^4+1\right)+32x^4\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-\left(4x^3-4x\right)^2\)
\(=\left(x^4+4x^3+8x^2-4x+1\right)\left(x^4-4x^3+8x^2+4x+1\right)\)
d)\(x^4+6x^3+7x^2-6x+1\)
\(=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)
\(=\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)\(=\left(x^2+3x-1\right)^2\)
a) 4x4 - 37x2 + 9 = (4x4 - 36x2) - (x2 - 9)
= 4x2(x2 - 9) - (x2 - 9)
= (4x2 - 1)(x2 - 9)
= (2x - 1)(2x + 1)(x - 3)(x + 3)
b) x4 - 13x2 + 36
= x4 - 4x2 - 9x2 + 36
= x2(x2 - 4) - 9(x2 - 4)
= (x2 - 9)(X2 - 4)
= (x - 3)(x + 3)(x - 2)(x + 2)
c) x4 - 8x2 + 7
= x4 - 7x2 - x2 + 7
= x2(x2 - 7) - (x2 - 7)
= (x2 - 1)(x2 - 7)
= (x - 1)(x + 1)(x2 - 7)
d) x4 - 7x2y2 + 12y4
= x4 - 3x2y2 - 4x2y2 + 12y4
= x2(x2 - 3y2) - 4y2(x2 - 3y2)
= (x2 - 4y2)(x2 - 3y2)
= (x - 2y)(x + 2y)(x2 - 3y2)
Bài làm :
a) 4x4 - 37x2 + 9 = (4x4 - 36x2) - (x2 - 9)
= 4x2(x2 - 9) - (x2 - 9)
= (4x2 - 1)(x2 - 9)
= (2x - 1)(2x + 1)(x - 3)(x + 3)
b) x4 - 13x2 + 36
= x4 - 4x2 - 9x2 + 36
= x2(x2 - 4) - 9(x2 - 4)
= (x2 - 9)(X2 - 4)
= (x - 3)(x + 3)(x - 2)(x + 2)
c) x4 - 8x2 + 7
= x4 - 7x2 - x2 + 7
= x2(x2 - 7) - (x2 - 7)
= (x2 - 1)(x2 - 7)
= (x - 1)(x + 1)(x2 - 7)
d) x4 - 7x2y2 + 12y4
= x4 - 3x2y2 - 4x2y2 + 12y4
= x2(x2 - 3y2) - 4y2(x2 - 3y2)
= (x2 - 4y2)(x2 - 3y2)
= (x - 2y)(x + 2y)(x2 - 3y2)