Question

a) \(x^4+2x^3+x^2\)

b) \(x^2+5x-6\)

c) \(5x\left(x-1\right)=x-1\)

d) \(x^4+8x\)

e) \(x^2+x-6\)

f) \(x^2-2x-3=0\)

h) \(2x^2+5x-3=0\)

Answer 1

\(a,x^4+2x^3+x^2=\left(x^2+x\right)^2\)

\(b,x^2+5x-6=x^2-x+6x-6=x\left(x-1\right)+6\left(x-1\right)\)\(=\left(x-1\right)\left(x+6\right)\)

\(c,5x\left(x-1\right)=x-1\Leftrightarrow5x\left(x-1\right)-\left(x-1\right)=0\Leftrightarrow\left(5x-1\right)\left(x-1\right)=0\)\(x^4+8x=x\left(x^3+8\right)=x\left(x+2\right)\left(x^2-2x+4\right)\) \(e,x^2+x-6=x^2+3x-2x-6=x\left(x+3\right)-2\left(x+3\right)=\left(x-2\right)\left(x+3\right)\)\(f,x^2-2x-3=x^2-3x+x-3=x\left(x-3\right)+\left(x-3\right)=\left(x+1\right)\left(x-3\right)\)\(h,2x^2+5x-3=0\Leftrightarrow2x^2-6x+x-3=0\Leftrightarrow2x\left(x-3\right)+\left(x-3\right)=0\Leftrightarrow\left(2x+1\right)\left(x-3\right)=0\)