a,
\\(x^4+2x^3+x^2\\\\ =x^4+x^3+x^3+x^2\\\\ =x^3\\left(x+1\\right)+x^2\\left(x+1\\right)\\\\ =\\left(x^3+x^2\\right)\\left(x+1\\right)=x^2\\left(x+1\\right)^2\\)
b,
\\(x^2-7x+12\\\\ =x^2-3x-4x+12\\\\ =x\\left(x-3\\right)+\\left(-4\\right)\\left(x-3\\right)\\\\ =\\left[x+\\left(-4\\right)\\right]\\left(x-3\\right)\\\\ =\\left(x-4\\right)\\left(x-3\\right)\\)
c,
\\(x^2-5x-14\\\\ =x^2+2x-7x-14\\\\ =x^2+2x-\\left(7x+14\\right)\\\\ =x\\left(x+2\\right)-7\\left(x+2\\right)\\\\ =\\left(x-7\\right)\\left(x+2\\right)\\)
d,
\\(4x^2-3x-1\\\\ =4x^2-4x+x-1\\\\ =4x\\left(x-1\\right)+\\left(x-1\\right)\\\\ =\\left(4x+1\\right)\\left(x-1\\right)\\)
a)x\(^4\)+2x\(^{^{ }3}\)+x\(^2\)
=x\(^2\)(x\(^2\)+2x+1\(^2\))
=x\(^2\)(x+1)\(^2\)
b)x\(^2\)-7x+12
=(x\(^2\)-2x3,5+3,5\(^2\))-0,25
=(x+3,5)\(^2\)-0,25
c)x\(^2\)-5x-14
=-(x\(^2\)+2x2,5+2,5\(^2\))+7,75
=-(x+2,5)\(^2\)+7,75
d)4x\(^2\)-3x-1
=-((2x)\(^2\)+22x1+1\(^2\))-1
=-(2x+1)\(^2\)-1
