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#)Giải :
\(x^3-2x-4\)
\(=x^3+2x^2-2x^2+2x-4x-4\)
\(=x^3+2x^2+2x-2x^2-4x-4\)
\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(x^4+2x^3+5x^2+4x-12\)
\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)
\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)
Câu 1.
Đoán được nghiệm là 2.Ta giải như sau:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
a)x3+x2+4
=x3-x2+2x+2x2-2x+4
=x(x2-x+2)+2(x2-x+2)
=(x+2)(x2-x+2)
b)x3-2x-4
=x3+2x2+2x-2x2-4x-4
=x(x2+2x+2)-2(x2+2x+2)
=(x-2)(x2+2x+2)
\(x^4+2x^2-24=x^4-4x^2+2x^2-24+4x^2=\left(x^4-4x^2\right)+\left(6x^2-24\right)\)
\(=x^2\left(x^2-4\right)+6\left(x^2-4\right)=\left(x^2+6\right)\left(x^2-4\right)=\left(x^2+6\right)\left(x-2\right)\left(x+2\right)\)
khó quá mk nản chí rùi huhu!!
3463465655775676876897756232544545465657578768
\(x^8+x^7+1\)
\(=x^8+x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-xx+1\)
\(=\left(x^8-x^6+x^5-x^3+x^2\right)\)
\(+\left(x^7-x^5+x^4-x^2+x\right)\)
\(+\left(x^6-x^4+x^3-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
\(x^4+2x^2-24\)
\(=x^4-4x^2+6x^2-24\)
\(=x^2\left(x^2-4\right)+6\left(x^2-4\right)\)
\(=\left(x^2+6\right)\left(x^2-4\right)\)
\(=\left(x^2+6\right)\left(x-2\right)\left(x+2\right)\)
a) \(x^4+4=x^4+4x^2+4-4\)
\(=\left(x^2+2\right)^2-4x^2=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)
b) \(B=\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)
Đặt \(x^2+5x+5=t\)
Khi đó ta có: \(B=\left(t-1\right)\left(t+1\right)-24=t^2-25=\left(t-5\right)\left(t+5\right)\)
Thay trở lại ta được:
\(B=\left(x^2+5x\right)\left(x^2+5x+10\right)=x\left(x+5\right)\left(x^2+5x+10\right)\)
a) 5x^2 + 6xy + y^2
=5x2+5xy+xy+y2
=5x.(x+y)+y.(x+y)
=(x+y)(5x+y)
b) x^2 + 2xy - 15y^2.
=x2-3xy+5xy-15y2
=x.(x-3y)+5y.(x-3y)
=(x-3y)(x+5y)
c) (x-y)^2 + 4(x-y) - 12
=(x-y)2+4(x-y)+4-16
=(x-y+2)2-16
=(x-y+2-4)(x-y+2+4)
=(x-y-2)(x-y+6)
d) x^3 - 2x - 4.
=x3+2x2+2x-2x2-4x-4
=x.(x2+2x+2)-2.(x2+2x+2)
=(x2+2x+2)(x-2)