a: Ta có: \(-3x^4+20x^3-35x^2-10x+48\)

\(=-\left(3x^4-20x^3+35x^2+10x-48\right)\)

\(=-\left(3x^4-9x^3-11x^3+33x^2+2x^2-6x+16x-48\right)\)

\(=-\left(x-3\right)\left(3x^3-11x^2+2x+16\right)\)

\(=-\left(x-3\right)\left(3x^3-6x^2-5x^2+10x-8x+16\right)\)

\(=-\left(x-3\right)\left(x-2\right)\left(3x^2-5x-8\right)\)

\(=-\left(x-3\right)\left(x-2\right)\left(3x-8\right)\left(x+1\right)\)

b: Ta có: \(-\left(2x^4+7x^3+x^2-7x-3\right)\)

\(=-\left(2x^4-2x^3+9x^3-9x^2+10x^2-10x+3x-3\right)\)

\(=-\left(x-1\right)\left(2x^3+9x^2+10x+3\right)\)

\(=-\left(x-1\right)\left(2x^3+2x^2+7x^2+7x+3x+3\right)\)

\(=-\left(x-1\right)\left(x+1\right)\left(2x^2+7x+3\right)\)

\(=-\left(x-1\right)\left(x+1\right)\cdot\left(x+3\right)\left(2x+1\right)\)

\(b,x^3-3x^2-4x+12\)

\(\Leftrightarrow x^2\left(x-3\right)-4\left(x-3\right)\)

\(\Leftrightarrow\left(x-3\right)\left(x^2-4\right)\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(x+2\right)\)

\(c,3x^3-7x^2+17x-5\)

\(\Leftrightarrow3x^3-x^2-6x^2+2x+15x-5\)

\(\Leftrightarrow x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)

\(\Leftrightarrow\left(3x-1\right)\left(x^2-2x+5\right)\)

\(\text{d) 2x}^4- 7x^3 - 2x^2 + 13x + 6\)
\(\text{= (2x^4 + 2x^3) - (9x^3 + 9x^2) + (7x^2 + 7x) + (6x + 6)}\)
\(\text{= 2x^3(x + 1) - 9x^2(x + 1) + 7x(x + 1) + 6(x + 1)}\)
\(\text{= (x + 1)(2x^3 - 9x^2 + 7x + 6)}\)
\(\text{= (x + 1)(2x + 1)(x - 3)(x - 2)}\)

phần b,c thay ''<=>'' là ''='' nhé ! Mình nhầm!

\(2x^4+7x^3-2x^2-13x+6\)

\(=2x^4+6x^3+x^3+3x^2-5x^2-15x+2x+6\)

\(=2x^3\left(x+3\right)+x^2\left(x+3\right)-5x\left(x+3\right)+2\left(x+3\right)\)

\(=\left(2x^3+x^2-5x+2\right)\left(x+3\right)\)

\(=\left(2x^3+4x^2-3x^2-6x+x+2\right)\left(x+3\right)\)

\(=\left[2x^2\left(x+2\right)-3x\left(x+2\right)+\left(x+2\right)\right]\left(x+3\right)\)

\(=\left(2x^2-3x+1\right)\left(x+2\right)\left(x+3\right)\)

\(=\left(2x^2-2x-x+1\right)\left(x+2\right)\left(x+3\right)\)

\(=\left[2x\left(x-1\right)-\left(x-1\right)\right]\left(x+2\right)\left(x+3\right)\)

\(=\left(2x-1\right)\left(x-1\right)\left(x+2\right)\left(x+3\right)\)

2x⁴-7x³-2x²+13x+6=2x⁴-2x³-5x³+5x²-7x²+7x+6x+6=2x³(x-1)-5x²(x-1)-7x(x-1)+6(x+1)=(x-1)(2x³-5x²-7x)+6(x+1)=(x-1)(2x³+2x²-7x²-7x)+6(x+1)                       =(x-1)(2x²(x+1)-7x(x+1))+6x(x+1)=(x-1)(x+1)(2x²-7x)+6(x+1)                                 =(x+1)(2x³-7x²-2x²+7x+6)=(x+1)(2x³-9x²+7x+6)=(x+1)(2x³-6x²-3x²+9x-2x+6)       =(x+1)(2x²(x-3)-3x(x-3)-2(x-3))=(x+1)(x-3)(2x²-3x-2)=(x+1)(x-3)(2x²-4x+x-2)          =(x+1)(x-3)(2x(x-2)+(x-2))                                                                                  =(x+1)(x-3)(x-2)(2x+1)

do hk biết ghi dấu ngoặc vuông nên bài làm hơi rối nhan,nhưng trình bày zô là thấy đơn giản àk,đúng thì chọn đúng nhan

Uhm, thanks bạn, bạn siêu quá =)

\(a^5-a\)

\(=a\left(a^4-1\right)\)

\(=a\left(a^2-1\right)\left(a^2+1\right)\)

\(=a\left(a-1\right)\left(a+1\right)\left(a^2+1\right)\)

\(b,=x^4-2x^3-x^3+2x^2+3x^2-6x-3x+6\\ =\left(x-2\right)\left(x^3-x^2+3x-3\right)\\ =\left(x-2\right)\left(x-1\right)\left(x^2+3\right)\\ c,=x^4-2x^3+4x^3-8x^2+4x^2-8x+3x-6\\ =\left(x-2\right)\left(x^3+4x^2+4x+3\right)\\ =\left(x-2\right)\left(x^3+3x^2+x^2+3x+x+3\right)\\ =\left(x-2\right)\left(x+3\right)\left(x^2+x+1\right)\)