\(a,a^4+a^2+1\)
\(=\left(a^2\right)^2+2a^2+1-a^2\)
\(=\left(a^2+1\right)^2-a^2\)
\(=\left(a^2+1-a\right)\left(a^2+1+a\right)\)
\(---\)
\(b,a^4+a^2-2\)
\(=a^4-a^2+2a^2-2\)
\(=a^2\left(a^2-1\right)+2\left(a^2-1\right)\)
\(=\left(a^2-1\right)\left(a^2+2\right)\)
\(=\left(a-1\right)\left(a+1\right)\left(a^2+2\right)\)
\(---\)
\(c,x^3-5x^2-14x\)
\(=x^3+2x^2-7x^2-14x\)
\(=x^2\left(x+2\right)-7x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-7x\right)\)
\(=x\left(x+2\right)\left(x-7\right)\)
\(a.a^4+a^2+1\)
\(=\left(a^4+2a^2+1\right)-a^2\)
\(=\left(a^2+1\right)^2-a^2\)
\(=\left(a^2+1+a\right)\left(a^2+1-a\right)\)
\(b.a^4+a^2-2\)
\(=a^4+2a^2-a^2-2\)
\(=a^2\left(a^2+2\right)-\left(a^2-2\right)\)
\(=\left(a^2+2\right)\left(a^2-1\right)\)
\(=\left(a^2+2\right)\left(a-1\right)\left(a+1\right)\)
\(c.x^3-5x^2-14x\)
\(=x^3+2x^2-7x^2-14\)
\(=x^3\left(x+2\right)-7x\left(x+2\right)\)
\(=\left(x^3-7x\right)\left(x+2\right)\)
\(=x\left(x-7x\right)\left(x+2\right)\)
