Câu 2: 

\(2\left(3x-4\right)-3\left(2x+3\right)+\left(3-5x\right)-\left(-4x+2\right)=0\)

\(\Leftrightarrow6x-8-6x-9+3-5x+4x-2=0\)

=>-x-16=0

=>x=-16

a) f(x) = -15x³+5x⁴-4x²+8x²-9x³-x⁴+15-7x³

= (5x⁴-x⁴)-(15x³+9x³+7x³)+(8x²-4x²)+15

= 4x⁴-31x³+4x²+15

b) f(1)= 4.1⁴-31.1³+4.1²+15 = -8

f(-1) = 4.(-1)⁴-31.(-1)³+4.(-1)²+15 = 54

a) f(x) = 4x⁴ - 31x³ = 4x² +15;

b)f(1) = -8 ; f(-1) = 54.

2: Ta có: \(x^4-4x^3-9x^2+8x+4=0\)

\(\Leftrightarrow x^4-x^3-3x^3+3x^2-12x^2+12x-4x+4=0\)

\(\Leftrightarrow x^3\left(x-1\right)-3x^2\left(x-1\right)-12x\left(x-1\right)-4\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3-3x^2-12x-4\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3+2x^2-5x^2-10x-2x-4\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x+2\right)-5x\left(x+2\right)-2\left(x+2\right)\right]=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x^2-5x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+2=0\\x^2-5x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\\x=\dfrac{5-\sqrt{33}}{2}\\x=\dfrac{5+\sqrt{33}}{2}\end{matrix}\right.\)

Vậy: \(S=\left\{1;-2;\dfrac{5-\sqrt{33}}{2};\dfrac{5+\sqrt{33}}{2}\right\}\)

1: Ta có: \(x^4+5x^3+10x^2+15x+9=0\)

\(\Leftrightarrow x^4+x^3+4x^3+4x^2+6x^2+6x+9x+9=0\)

\(\Leftrightarrow x^3\left(x+1\right)+4x^2\left(x+1\right)+6x\left(x+1\right)+9\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x^3+4x^2+6x+9\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left[x^3+3x^2+x^2+6x+9\right]=0\)

\(\Leftrightarrow\left(x+1\right)\left[x^2\left(x+3\right)+\left(x+3\right)^2\right]=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+3\right)\left(x^2+x+3\right)=0\)

mà \(x^2+x+3>0\forall x\)

nên (x+1)(x+3)=0

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\)

Vậy: S={-1;-3}

giúp mình vs ạ

a. Rút gọn đa thức và sắp xếp theo thứ tự giảm dần của biến..

\(A\left(x\right)=13x^4+3x^2+15x+7x^2-10x^4-7x-6-8x+15\)

\(=\left(13x^4-10x^4\right)+\left(3x^2+7x^2\right)+\left(15x-7x-8x\right)+\left(15-6\right)\)

\(=3x^4+10x^2+9.\)

\(B\left(x\right)=5x^4+10-5x^2-18+3x-10x^2-3x-4x^4\)

\(=\left(5x^4-4x^4\right)+\left(-5x^2-3x^2\right)+\left(3x-3x\right)+\left(10-18\right)\)

\(=x^4-8x^2-8\)

b. Tính M = A(x) + B(x) ; N = A(x) - B(x)

\(M=A\left(x\right)+B\left(x\right)=\left(3x^4+10x^2+9\right)+\left(x^4-8x^2-8\right)\)

\(=\left(3x^4+x^4\right)+\left(10x^2-8x^2\right)+\left(10-8\right)\)

\(=4x^4+2x^2+2\)

\(N=A\left(x\right)-B\left(x\right)=\left(3x^4+10x^2+9\right)-\left(x^4-8x^2-8\right)\)

\(=3x^4+10x^2+9-x^4+8x^2+8\)

\(=\left(3x^4-x^4\right)+\left(10x^2+8x^2\right)+\left(9+8\right)\)

\(=2x^4+18x^2+17\)

a. x³+4x²-29x+24