Question

1. x² - 9 + 3x ( x - 3 ) 2. x⁴ + 5x² + 4x + 5 3. x⁴ + x² + 1 minh cam on

Answer 1

1: x^2-9+3x(x-3)

=(x-3)(x+3)+3x(x-3)

=(x-3)(x+3+3x)

=(4x+3)(x-3)

2: =x^4+5x^2+4x+5

=x^4+x^3+x^2-x^3-x^2-x+5x^2+5x+5

=(x^2+x+1)(x^2-x+5)

3: =x^4+2x^2+1-x^2

=(x^2+1)^2-x^2

=(x^2-x+1)(x^2+x+1)

Answer 2

1) \(x^2-9+3x\left(x-3\right)\)

\(=\left(x^2-9\right)+3x\left(x-3\right)\)

\(=\left(x+3\right)\left(x-3\right)+3x\left(x-3\right)\)

\(=\left(x-3\right)\left(x+3+3x\right)\)

\(=\left(x-3\right)\left(4x+3\right)\)

2) \(x^4+5x^2+4x+5\)

\(=x^4+x^3+x^2-x^3-x^2-x+5x^2+5x+5\)

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

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

3) \(x^4+x^2+1\)

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

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

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