a) x4 + x2 + 1 = (x4 + 2x2 + 1) - x2 = (x2 + 1) - x2 = (x2 + x + 1)(x2 - x + 1)
b) x2 - 3x + 2 = (x2 - x) - (2x - 2) = x(x - 1) - 2(x - 1) = (x - 2)(x - 1)
c) x2 - 7x + 10 = (x2 - 5x) - (2x - 10) = x(x - 5) - 2(x - 5) = (x - 2)(x - 5)
d) 4x4 + 1 = (4x4 + 4x2 + 1) - 4x2 = (2x2 + 1)2 - 4x2 = (2x - 2x + 1)(2x + 2x + 1)
\(b.x^2-3x+2\)
\(\Leftrightarrow\left(x^2-2x\right)-\left(x-2\right)\)
\(\Leftrightarrow x\left(x-2\right)\left(x-2\right)\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\)
\(c.x^2-7x+10\)
\(\Leftrightarrow\left(x^2-5x\right)-\left(2x-10\right)\)
\(\Leftrightarrow x\left(x-5\right)-2\left(x-5\right)\)
\(\Leftrightarrow\left(x-2\right)\left(x-5\right)\)
