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a)\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b)\(\left(x-3\right)\left(x-7\right)\left(x+2\right)\)
c)\(\left(x-3\right)\left(x+3\right)\left(x+2\right)\left(x+1\right)\)
d)\(\left(x+5\right)\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
a) x3 + 6x2 + 11x + 6
= (x3 + x2) + (5x2 + 5x) + (6x + 6)
= x2(x + 1) + 5x(x + 1) + 6(x + 1)
= (x2 + 5x + 6)(x + 1)
= (x2 + 2x + 3x + 6)(x + 1)
= [x(x + 2) + 3(x + 2)](x + 1)
= (x + 3)(x + 2)(x + 1)
b) x3 - 8x2 + x + 42
= x3 + 2x2 - 10x2 - 20x + 21x + 42
= x2(x + 2) - 10x(x + 2) + 21(x + 2)
= (x2 - 10x + 21)(x + 2)
= (x2 - 3x - 7x + 21)(x + 2)
=[x(x - 3) - 7(x - 3)](x + 2)
=(x - 7)(x - 3)(x + 2)
c) x4 + 3x3 - 7x2 - 27x - 18
= x4 + x3 + 2x3 + 2x2 - 9x2 - 9x - 18x - 18
= x3(x + 1) + 2x2(x + 1) - 9x(x + 1) - 18(x + 1)
= (x3 + 2x2 - 9x - 18)(x + 1)
= [x2(x + 2) - 9(x + 2)](x + 1)
=(x2 - 9)(x + 2)(x + 1)
= (x - 3)(x + 3)(x + 2)(x + 1)
d) x4 + 5x3 - 7x2 - 41x - 30
= x4 + x3 + 4x3 + 4x2 - 11x2 - 11x - 30x - 30
= x3(x + 1) + 4x2(x + 1) - 11x(x + 1) -30(x + 1)
= (x3 + 4x2 - 11x - 30)(x + 1)
= (x3 + 2x2 + 2x2 + 4x - 15x - 30)(x + 1)
= [x2(x + 2) + 2x(x + 2) - 15(x +2)](x + 1)
=(x2 + 2x - 15)(x + 2)(x + 1)
= (x2 - 3x + 5x - 15)(x + 2)(x +1)
= [x(x - 3) + 5(x - 3)](x + 2)(x + 1)
= (x - 3)(x + 5)(x + 2)(x + 1)
NHỚ TIK CHO MIK NHA, đừng có mà đọc suông xong bỏ đi đấy. mik là đầy đủ hơn cái bn ở dưới nên cho mik nhiều tik hơn nhé
a, \(x^4+6x^3+7x^2-6x+1\)
\(=x^4-2x^2+1+6x^3+9x^2+6x\)
\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)
\(=\left(x^2-1+3x\right)^2\)
b, \(x^4-7x^3+14x^2-7x+1\)
\(=x^4+2x^2+1+7x^3+12x^2-7x\)
\(=\left(x^2+1\right)^2-7x\left(x^2+1\right)+12^2\)
\(=\left(x^2-1+3x\right)^2\)
c, \(12x^2-11x-36\)
\(=12x^2-27x+16x-36\)
\(=3x\left(4x-9\right)+4\left(4x-9\right)\)
\(=\left(4x-9\right)\left(3x+4\right)\)
mk ghi đáp án, còn lại bạn tự biến đổi
a) \(2x^3-x^2+5x+3=\left(2x+1\right)\left(x^2-x+3\right)\)
b) \(x^3+5x^2+8x+4=\left(x+1\right)\left(x+2\right)^2\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
d) \(4x^4+1=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
e) \(x^4-7x^3+14x^2-7x+1=\left(x^2-4x+1\right)\left(x^2-3x+1\right)\)
mk làm chi tiết theo yêu của của người hỏi đề:
a) \(2x^3-x^2+5x+3\)
\(=\left(2x^3-2x^2+6x\right)+\left(x^2-x+3\right)\)
\(=2x\left(x^2-x+3\right)+\left(x^2-x+3\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
b) \(x^3+5x^2+8x+4\)
\(=\left(x^3+4x^2+4x\right)+\left(x^2+4x+4\right)\)
\(=x\left(x^2+4x+4\right)+\left(x^2+4x+4\right)\)
\(=\left(x+1\right)\left(x^2+4x+4\right)\)
\(=\left(x+1\right)\left(x+2\right)^2\)
\(x^3-x^2-14x+24\)
\(=x^3-2x^2+x^2-2x-12x+24\)
\(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-2\right).\left[x^2+4x-3x-12\right]\)
\(=\left(x-2\right).\left[x\left(x+4\right)-3\left(x+4\right)\right]\)
\(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)
\(x^4+x^3+2x-4\)
\(=x^4-x^3+2x^3-2x^2+2x^2-2x+4x-4\)
\(=x^3\left(x-1\right)+2x^2\left(x-1\right)+2x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+2x^2+2x+4\right)\)
\(=\left(x-1\right).\left[x^2\left(x+2\right)+2\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+2\right)\)
\(8x^4-2x^3-3x^2-2x-1\)
\(=8x^4-8x^3+6x^3-6x^2+3x^2-3x+x-1\)
\(=8x^3\left(x-1\right)+6x^2\left(x-1\right)+3x\left(x-1\right)+x-1\)
\(=\left(x-1\right)\left(8x^3+6x^2+3x+1\right)\)
\(=\left(x-1\right)\left[\left(8x^3+1\right)+\left(6x^2+3x\right)\right]\)
\(=\left(x-1\right)\left[\left(2x+1\right)\left(4x^2-2x+1\right)+3x\left(2x+1\right)\right]\)
\(=\left(x-1\right)\left(2x+1\right)\left(4x^2+x+1\right)\)
\(3x^2-7x+2\)
\(=3x^2-6x-x+2\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
Chúc bạn học tốt.
\(x^3-5x^2-14x\)
\(=x^3+2x^2-7x^2-14x\)
\(=x^2\left(x+2\right)-7x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-7x\right)\)
\(=x\left(x+2\right)\left(x-7\right)\)
\(x^3-7x-6\)
\(=x^3+x^2-x^2-x-6x-6\)
\(=x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+1\right)\left(x^2+2x-3x-6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)-3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)
\(x^3-19x-30\)
\(=x^3-5x^2+5x^2-25x+6x-30\)
\(=x^2\left(x-5\right)+5x\left(x-5\right)+6\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2+5x+6\right)\)
\(=\left(x-5\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x-5\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x-5\right)\left(x+3\right)\left(x+2\right)\)
c)x12+x6+1
Lần lượt thêm và bớt x9; x3;x6 ta đc:
=x12+x9-x6-x9-x6-x3+x6+x3+1
=x6(x6+x3+1)-x3(x6+x3+1)+(x6+x3+1)
=(x6-x3+1)(x6+x3+1)
b)x4-7x3-14x2-7x+1
=x4-3x3+x2-4x3+12x2-4x+x2-3x+1
=x2(x2-3x+1)-4x(x2-3x+1)+(x2-3x+1)
=(x2-4x+1)(x2-3x+1)
=X4-3X3 +6X3-18X2+11X2-33X+6X-18
=(X-3)(X3+6X2+11X+6)
=(X-3)(X+3)(X+1)(X+2)
\(x^4+3x^3-7x^2-27x-18.\)
\(=\left(x^4-9x^2\right)+\left(3x^3-27x\right)+\left(2x^2-18\right)\)
\(=x^2\left(x-3\right)\left(x+3\right)+3x\left(x-3\right)\left(x+3\right)+2\left(x-3\right)\left(x+3\right).\)
\(=\left(x-3\right)\left(x+3\right)\left(x^2+3x+2\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x^2+x+2x+2\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x+1\right)\left(x+2\right).\)
\(g,x^2-2xy+y^2-9z^2=\left(x-y\right)^2-\left(3z\right)^2\)\(=\left(x-y+3z\right)\left(x-y-3z\right)\)
\(h,5x^4-20x^2=5x^2\left(x^2-4\right)=5x^2\left(x-2\right)\left(x+2\right)\)
\(i,7x^2-7y^2-14x+14y=7\left(x-y\right)\left(x+y\right)-14\left(x-y\right)\)
\(=\left(x-y\right)\left(7x+7y-14\right)=7\left(x-y\right)\left(x+y-2\right)\)
\(k,x^2+8x+3x+24=x\left(x+8\right)+3\left(x+8\right)=\left(x+8\right)\left(x+3\right)\)
\(m,x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
\(n,x^6-y^6=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)=\left(x-y\right)\left(x+y\right)\left(x^4+x^2y^2+y^4\right)\)
a) \(x^4+3x^3-7x^2-27x-18\)
\(=\left(x^4+3x^3+2x^2\right)-\left(9x^2-27x-18\right)\)
\(=x^2\left(x^2+3x+2\right)-9\left(x^2+3x+2\right)=\left(x^2+x+2x+2\right)\left(x^2-9\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\left(x+3\right)\)
b) \(x^4+5x^3-7x^2-41x-30\)
\(=\left(x^4+2x^3-15x^2\right)+\left(3x^3+6x^2-45x\right)+\left(2x^2+4x-30\right)\)
\(=x^2\left(x^2+2x-15\right)+3x\left(x^2+2x-15\right)+2\left(x^2+2x-15\right)\)
\(=\left(x^2+2x-15\right)\left(x^2+3x+2\right)=\left(x^2+5x-3x-15\right)\left(x^2+x+2x+2\right)\)
\(=\left(x+5\right)\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
c) \(x^6-14x^4+49x^2-36\)
\(=\left(x^6-9x^4\right)+\left(-5x^4+45x^2\right)+\left(4x^2-36\right)\)
\(=x^4\left(x^2-9\right)-5x^2\left(x^2-9\right)+4\left(x^2-9\right)\)
\(=\left(x^2-9\right)\left(x^4-5x^2+4\right)=\left(x^2-9\right)\left(x^4-4x^2-x^2+4\right)\)
\(=\left(x^2-1\right)\left(x^2-4\right)\left(x^2-9\right)=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\left(x-3\right)\left(x+3\right)\)