Question

a . x^2 - 4x + 3

b. x^2 + x - 6

c. x^2 - 5x + 6

d. x^4+4

Answer 1

a ) \(x^2-4x+3=x^2-3x-x+3=x\left(x-3\right)-\left(x-3\right)=\left(x-1\right)\left(x-3\right)\)

b ) \(x^2+x-6=x^2+3x-2x-6=x\left(x+3\right)-2\left(x+3\right)=\left(x-2\right)\left(x+3\right)\)

c ) \(x^2-5x+6=x^2-3x-2x+6=x\left(x-3\right)-2\left(x-3\right)=\left(x-2\right)\left(x-3\right)\)

d ) \(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

\(=\left(x^2+2\right)^2-\left(2x\right)^2\)

\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)