Question

Phân tích các đa thức sau thành nhân tử

a, 27x³ - \(\dfrac{1}{27}\)

b, x³+ 4x² - 29x + 24

c, x² + 7x + 12

d, 3x² - 3xy - 5x + 5y

Answer 1

a)\(\left(3x\right)^3-\left(\dfrac{1}{3}\right)^3=\left(3x-\dfrac{1}{3}\right)\left(9x^2+x+\dfrac{1}{9}\right)\)

b)\(x^3-x^2+5x^2-5x-24x+24\)

\(=x^2\left(x-1\right)+5x\left(x-1\right)-24\left(x-1\right)\)

\(=\left(x^2+5x-24\right)\left(x-1\right)\)

\(=\left(x^2+8x-3x-24\right)\left(x-1\right)\)

\(=\left[x\left(x+8\right)-3\left(x+8\right)\right]\left(x-1\right)\)

\(=\left(x-3\right)\left(x+8\right)\left(x-1\right)\)

c)\(x^2+7x+12=x^2+3x+4x+12\)

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

d)\(3x^2-3xy-5x+5y\)

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