Question

Phân tích đa thức thành nhân tử bằng pp bổ sung hằng đẳng thức

a/ \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)

b/ \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{1}{4}-2\)

Answer 1

a) \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}=\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)

b) \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{1}{4}-2=\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)

Answer 2

a, \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)

\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{2}^2\)

\(=\left(x-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{3}{2}\right)\)

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

b, \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{1}{4}-2\)

\(=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)

\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{2}^2\)

\(=\left(x-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{3}{2}\right)\)

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

Chúc bạn học tốt!!!