Bài 3:
\(a)\left(x+2\right)\left(x+3\right)-\left(x-2\right)\left(x+5\right)=0\\ \Leftrightarrow x^2+3x+2x+6-\left(x^2+5x-2x-10\right)=0\\ \Leftrightarrow x^2+5x+6-x^2-3x+10=0\\ \Leftrightarrow2x+16=0\\ \Leftrightarrow2x=-16\\ \Leftrightarrow x=-\dfrac{16}{2}=-8\\ b)\left(x-3\right)\left(x-2\right)-\left(x+1\right)\left(x-5\right)=0\\ \Leftrightarrow\left(x^2-2x-3x+6\right)-\left(x^2-5x+x-5\right)=0\\ \Leftrightarrow x^2-5x+6-x^2+4x+5=0\\ \Leftrightarrow-x+11=0\\ \Leftrightarrow x=11\\ c)x\left(2x-5\right)-2x\left(x-6\right)=42\\ \Leftrightarrow2x^2-5x-2x^2+12x=42\\ \Leftrightarrow7x=42\\ \Leftrightarrow x=\dfrac{42}{7}\\ \Leftrightarrow x=6\\ d)\left(x-1\right)\left(2x+3\right)-2x\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(2x+3-2x\right)=0\\ \Leftrightarrow3\left(x-1\right)=0\\ \Leftrightarrow x-1=0\\ \Leftrightarrow x=1\)
Bài 2:
b: 
c:
d:
Bài 4:
a: \(A\left(x\right)=x^7-3x^2-x^5+x^4-x^2+2x-7\)
\(=x^7-x^5+x^4+\left(-3x^2-x^2\right)+2x-7\)
\(=x^7-x^5+x^4-4x^2+2x-7\)
\(B\left(x\right)=x-2x^2+x^4-x^5-x^7-4x^2-1\)
\(=-x^7-x^5+x^4+\left(-2x^2-4x^2\right)+x-1\)
\(=-x^7-x^5+x^4-6x^2+x-1\)
b: A(x)+B(x)
\(=x^7-x^5+x^4-4x^2+2x-7-x^7-x^5+x^4-6x^2+x-1\)
\(=-2x^5-10x^2+3x-8\)
A(x)-B(x)
\(=x^7-x^5+x^4-4x^2+2x-7+x^7+x^5-x^4+6x^2-x+1\)
\(=2x^7+2x^2+x-6\)
c: C(x)=A(x)+B(x
=>\(C\left(x\right)=-2x^5-10x^2+3x-8\)
Thay x=-1 vào C(x), ta được:
\(C\left(-1\right)=-2\cdot\left(-1\right)^5-10\cdot\left(-1\right)^2+3\cdot\left(-1\right)-8\)
=2-10-3-8
=-1-10-8=-19
