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\(A=4x^4+625\)
\(=4x^4+100x^2+625-100x^2\)
\(=\left(2x^2+25\right)^2-100x^2\)
\(=\left(2x^2+5x+25\right)\left(2x^2-5x+25\right)\)
#)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:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(4x^4-16-4x^2-16x\)
\(=4x^2\left(x^2-1\right)-16\left(1+x\right)\)
\(=4x^2\left(x+1\right)\left(x-1\right)-16\left(x+1\right)\)
\(=\left(x+1\right)\left[4x^2\left(x-1\right)-16\right]\)
\(=\left(x+1\right)4\left[x^2\left(x-1\right)-4\right]\)
Nguyễn Văn Tuấn AnhNs r, không biết thì not làm
\(4x^4-16-4x^2-16x\)
\(=4x^2\left(x^2-1\right)-16\left(x+1\right)\)
\(=4x^2\left(x-1\right)\left(x+1\right)-16\left(x+1\right)\)
\(=\left(x+1\right)\left[4x^2\left(x-1\right)-16\right]\)
\(=4\left(x+1\right)\left[x^2\left(x-1\right)-4\right]\)
\(=4\left(x+1\right)\left[x^3-x^2-4\right]\)
\(=4\left(x+1\right)\left[x^3+x^2+2x-2x^2-2x-4\right]\)
\(=4\left(x+1\right)\left[x\left(x^2+x+2\right)-2\left(x^2+x+2\right)\right]\)
\(=4\left(x+1\right)\left(x-2\right)\left(x^2+x+2\right)\)
\(4x^4+4x^3-x^2-x\)
\(=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=\left(x+1\right)\left(4x^3-x\right)\)
\(=x\left(x+1\right)\left(4x^2-1\right)\)
\(=x\left(x+1\right)\left[\left(2x\right)^2-1\right]\)
\(=x\left(x+1\right)\left(2x+1\right)\left(2x-1\right)\)
(Nhớ k cho mình với nhá!)
chịu....................??????????????????????????????????????????????????
x^2(1-x^2)-4-4x^2
=x^2-x^4-4-4x^2
=x^2-(x^2+1)^2
=(x-x^2-1)(x+x^2+1)
\(x^4+4x^3+2x^2-4x+1\)
\(=x^4+2x^3-x^2+2x^3+4x^2-2x-x^2-2x+1\)
\(=x^2\left(x^2+2x-1\right)+2x\left(x^2+2x-1\right)-\left(x^2+2x-1\right)\)
\(=\left(x^2+2x-1\right)^2\)
4x^4+81
= (2x^2)^2+9^2 +36x^2-36x^2
= (2x^2+9)^2 -36x^2
=( 2x^2+9-6x)(2x^2+9+6x)
\(4x^4+1=\left(2x^2\right)^2+2.2x^2+1-\left(2x\right)^2=\left(2x^2+1\right)^2-\left(2x\right)^2=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
\(4x^4+625\)
\(=\left(2x^2\right)^2+100x^2+25^2-100x^2\)
\(=\left(2x^2+25\right)^2-\left(10x\right)^2\)
\(=\left(2x^2+25+10x\right)\left(2x^2+25-10x\right)\)