Question

1. phân tích đa thức thành nhân tử

\(\left(x-7\right)\left(x-5\right)\left(x-4\right)\left(x-2\right)-72\)

2. tìm min của biểu thức

\(A=2x^2-x+2020\)

Answer 1

1.

\(=\left(x-7\right)\left(x-2\right)\left(x-4\right)\left(x-5\right)-72\)

\(=\left(x^2-9x+14\right)\left(x^2-9x+20\right)-72\)

\(=\left(x^2-9x+14\right)\left(x^2-9x+14+6\right)-72\)

\(=\left(x^2-9x+14\right)^2+6\left(x^2-9x+14\right)-72\)

\(=\left(x^2-9x+14\right)^2+12\left(x^2-9x+14\right)-6\left(x^2-9x+14\right)-72\)

\(=\left(x^2-9x+14\right)\left(x^2-9x+26\right)-6\left(x^2-9x+26\right)\)

\(=\left(x^2-9x+26\right)\left(x^2-9x+8\right)\)

\(=\left(x-1\right)\left(x-8\right)\left(x^2-9x+26\right)\)

2.

\(A=2\left(x^2-2.\frac{1}{4}x+\frac{1}{16}\right)+\frac{16159}{8}\)

\(A=2\left(x-\frac{1}{4}\right)^2+\frac{16159}{8}\ge\frac{16159}{8}\)