Question

Phân tích đa thức thành nhân tử:

a) x² - 7xy + 10y²

b) 5x² + 6xy + y²

c) x² - 5x - 14

d) x² + 2x - 15

Answer 1

a) Ta có: \(x^2-7xy+10y^2\)

\(=x^2-2xy-5xy+10y^2\)

\(=x\left(x-2y\right)-5y\left(x-2y\right)\)

\(=\left(x-2y\right)\left(x-5y\right)\)

b) Ta có: \(5x^2+6xy+y^2\)

\(=5x^2+5xy+xy+y^2\)

\(=5x\left(x+y\right)+y\left(x+y\right)\)

\(=\left(x+y\right)\left(5x+y\right)\)

c) Ta có: \(x^2-5x-14\)

\(=x^2-7x+2x-14\)

\(=x\left(x-7\right)+2\left(x-7\right)\)

\(=\left(x-7\right)\left(x+2\right)\)

d) Ta có: \(x^2+2x-15\)

\(=x^2+5x-3x-15\)

\(=x\left(x+5\right)-3\left(x+5\right)\)

\(=\left(x+5\right)\left(x-3\right)\)