Question

 Phân tích đa thức thành nhân tử : ( x- 3 )( x - 5)( x - 6 )(x - 10 ) -24x^2

Answer 1

\(\left(x-3\right)\left(x-10\right)\left(x-5\right)\left(x-6\right)-24x^2\)

\(=\left(x^2+30-13x\right)\left(x^2+30-11x\right)-24x^2\)

\(=\left(x^2+30x-12x-x\right)\left(x^2+30x-12x+x\right)-24x^2\)

\(=\left(x^2+30-12x\right)^2-x^2-24x^2\)

\(=\left(x^2-12x+30\right)^2-\left(5x\right)^2\)

\(=\left(x^2-12x+30+5x\right)\left(x^2-12x+30-5x\right)\)

\(=\left(x^2-7x+30\right)\left(x^2-17x+30\right)\)