a) Làm phép tính \(\left(15+5x^2-3x^3-9x\right):\left(5-3x\right)\)
b) t bằng mấy để \(x^3-3x^2+t-4x⋮\left(1+x+x^2\right)\)
a) Làm phép tính \(\left(15+5x^2-3x^2-9x\right):\left(5-3x\right)\)
b) t bằng mấy để \(x^3-3x^2+t-4x⋮\left(1+x+x^2\right)\)
a) Làm phép tính \(\left(15+5x^2-3x^2-9x\right):\left(5-3x\right)\)
b) t bằng mấy để \(x^3-3x^2+t-4x⋮\left(1+x+x^2\right)\)
a) \(\left(15+5x^2-3x^2-9x\right):\left(5-3x\right)\)
\(=\dfrac{2x^2-9x+15}{5-3x}\)
b) \(x^3-3x^2+t-4x⋮\left(1+x+x^2\right)\)
\(\Rightarrow x^3+x^2+x-4x^2-5x+t⋮x^2+x+1\)
\(\Rightarrow x\left(x^2+x+1\right)-4x^2-5x+t⋮x^2+x+1\)
\(\Rightarrow x\left(x^2+x+1\right)-4\left(x^2+x+1\right)-x+4+t⋮x^2+x+1\)
\(\Rightarrow\left(x-4\right)\left(x^2+x+1\right)-\left(x-4\right)+t⋮x^2+x+1\)
Đặt nhân tử chung rồi tự lm tiếp
Tính : \(\left(3x^3-5x^2+9x-15\right):\left(3x-5\right)\)
Tìm x : a ) \(\left(x+1\right)\left(x-2\right)-x\left(x-3\right)=0\)
b) \(x^2+4x+3=0\)
Vậy \(3x^2-5x^2+9x-15=\left(3x-5\right)\left(x^2+3\right)\)
b
\(\left(x+1\right)\left(x-2\right)-x\left(x-3\right)=0\)
\(\Leftrightarrow x^2-2x+x-2-x^2+3x=0\)
\(\Leftrightarrow2x-2=0\)
\(\Leftrightarrow x=1\)
b
\(x^2+4x+3=0\)
\(\Leftrightarrow\left(x^2+4x+4\right)-1=0\)
\(\Leftrightarrow\left(x+2\right)^2-1=0\)
\(\Leftrightarrow\left(x+3\right)\left(x+1\right)=0\)
\(\Leftrightarrow x=-1;x=-3\)
1. Làm tính chia :
\(\left(x^3+8y^3\right):\left(x+2y\right)\)
2. Tìm số tự nhiên n để phép chia sau là phép chia hết :
a) \(\left(5x^3-3x^2+x\right):3x^n\)
b) \(\left(12x^3y^7+9x^4y^5-3x^5y^8\right):3x^{n+1}y^{n+3}\)
giải pt:
a,\(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{-4x^2+16x-15}\)
b,\(\left(9x-2\right)\sqrt{3x-1}+\left(10-9x\right)\sqrt{3-3x}-4\sqrt{-9x^2+12x-3}=4\)
c, \(\left(6x-5\right)\sqrt{x+1}-\left(6x+2\right)\sqrt{x-1}+4\sqrt{x^2-1}=4x-3\)
Tìm x, biết:
a) \(\left(2x+3\right)\left(x-4\right)+\left(x-5\right)\left(x-2\right)=\left(3x-5\right)\left(x-4\right)\)
b) \(\left(8x-3\right)\left(3x+2\right)-\left(4x+7\right)\left(x+4\right)=\left(2x+1\right)\left(5x-1\right)\)
c) \(\left(3x-5\right)\left(7-5x\right)-\left(5x+2\right)\left(2-3x\right)=4\)
a) \(\left(2x+3\right)\left(x-4\right)+\left(x+5\right)\left(x-2\right)=\left(3x-5\right)\left(x-4\right)\)
\(\Leftrightarrow2x^2-8x+3x-12+x^2-2x-5x+10=3x^2-12x-5x+20\)
\(\Leftrightarrow2x^2-8x+3x-12+x^2-2x+10=3x^2-12x+20\)
\(\Leftrightarrow3x^2-7x-2=3x^2-12x+20\)
\(\Leftrightarrow-7x+12x=20+2\)
\(\Leftrightarrow5x=22\)
\(\Rightarrow x=\dfrac{22}{5}\)
tick cho mk nha
b) \(\left(8x-3\right)\left(3x+2\right)-\left(4x+7\right)\left(x+4\right)=\left(2x+1\right)\left(5x-1\right)\)
\(\Leftrightarrow24x^2+16x-9x-6-4x^2-23x-28=10x^2+3x-1\)
\(\Leftrightarrow20x^2-16x-34-10x^2-3x+1=0\)
\(\Leftrightarrow10x^2-19x-33=0\)
\(\Delta=\left(-19\right)^2-4.10.\left(-33\right)=1320\)
\(x_1=3;x_2=\dfrac{-11}{10}\)
Tick cho mk nha
c) \(\left(3x-5\right)\left(7-5x\right)-\left(5x+2\right)\left(2-3x\right)=4\)
\(\Leftrightarrow21x-15x^2-35+25x-4x+15x^2-4=4\)
\(\Leftrightarrow42x-39=4\)
\(\Leftrightarrow42x=4+39\)
\(\Leftrightarrow42x=43\)
\(\Rightarrow x=\dfrac{43}{42}\)
Tick cho mk nha
Bài 1: Thực hiện phép tính:
\(3x.\left(x^2-5x+\dfrac{1}{3}\right)\\ \left(x-2\right).\left(5x-1\right)\\ 5x.\left(3x^2-4x+1\right)\\ \left(x+3\right)\left(x^2+3x-5\right)\)
\(3x\left(x^2-5x+\dfrac{1}{3}\right)=3x.x^2+3x.\left(-5x\right)+3x.\dfrac{1}{3}=3x^3-15x^2+x\)
\(\left(x-2\right)\left(5x-1\right)=x.5x+x.\left(-1\right)+\left(-2\right).5x+\left(-2\right)\left(\right)-1=5x^2-x-10x+2=5x^2-11x+2\)
\(5x\left(3x^2-4x+1\right)=5x.3x^2+5x.\left(-4x\right)+5x.1=15x^3-20x^2+5x\)
\(\left(x+3\right)\left(x^2+3x-5\right)=x.x^2+x.3x+x\left(-5\right)+3.x^2+3.3x+3.\left(-5\right)=x^3+3x^2-5x+3x^2+9x-15=x^3+6x^2+4x-15\)
Tính:
\(a)\left(-2x^2\right)\cdot\left(3x-4x^3+7-x^2\right)\)
\(b)\left(x+3\right)\cdot\left(2x^2-3x-5\right)\)
\(c)\left(-6x^5+7x^4-6x^3\right):3x^3\)
\(d)\left(9x^2-4\right):\left(3x+2\right)\)
\(e)\left(2x^4-13x^3+15x^2+11x-3\right):\left(x^2-4x-3\right)\)
a: \(=-2x^2\cdot3x+2x^2\cdot4X^3-2x^2\cdot7+2x^2\cdot x^2\)
\(=8x^5+2x^4-6x^3-14x^2\)
b: \(=2x^3-3x^2-5x+6x^2-9x-15\)
\(=2x^3+3x^2-14x-15\)
c: \(=\dfrac{-6x^5}{3x^3}+\dfrac{7x^4}{3x^3}-\dfrac{6x^3}{3x^3}=-2x^2+\dfrac{7}{3}x-2\)
d: \(=\dfrac{\left(3x-2\right)\left(3x+2\right)}{3x+2}=3x-2\)
e: \(=\dfrac{2x^4-8x^3-6x^2-5x^3+20x^2+15x+x^2-4x-3}{x^2-4x-3}\)
=2x^2-5x+1
Bài 2 . Thực hiện phép tính
a)\(6x^3\)\(\left(\dfrac{1}{3}x^2-\dfrac{5}{2}-\dfrac{1}{6}\right)\)\(-2x^5\)\(-x^3\)
b)\(\left(x-3\right)\left(x^2+3x-2\right)\)
c)\(\left(4x^3-4x^2-5x+4\right):\left(2x+1\right)\)
a: =2x^5-15x^3-x^2-2x^5-x^3=-16x^3-x^2
b: =x^3+3x^2-2x-3x^2-9x+6
=x^3-11x+6
c: \(=\dfrac{4x^3+2x^2-6x^2-3x-2x-1+5}{2x+1}\)
\(=2x^2-3x-1+\dfrac{5}{2x+1}\)
a) \(6x^3\left(\dfrac{1}{3}x^2-\dfrac{5}{2}-\dfrac{1}{6}\right)-2x^5-x^3\)
\(=6x^3\left(\dfrac{1}{3}x^2-\dfrac{16}{6}\right)-2x^5-x^3\)
\(=2x^5-16x^3-2x^5-x^3\)
\(=-17x^3\)
b) \(\left(x+3\right)\left(x^2+3x-2\right)\)
\(=x^3+3x^2-2x+3x^2+9x-6\)
\(=x^3+6x^2+7x-6\)
c) \(\left(4x^3-4x^2-5x+4\right):\left(2x+1\right)\)
\(=2x^2+4x^3-2x-4x^2-\dfrac{5}{2}-5x+\dfrac{2}{x}+4\)
\(=4x^3-2x^2-7x+\dfrac{2}{x}+\dfrac{3}{2}\)