因式分解 a^3x^2-5a^3x+6a^3+x^2-5x+6

解答

因式分解

a^{3} x^{2} - 5 a^{3} x + 6 a^{3} + x^{2} - 5 x + 6

(x - 2) (x - 3) (a + 1) (a^{2} - a + 1)

求解步骤

a^{3} x^{2} - 5 a^{3} x + 6 a^{3} + x^{2} - 5 x + 6

= (x^{2} a^{3} - 5 x a^{3} + 6 a^{3}) + (x^{2} - 5 x + 6)

从

x^{2} a^{3} - 5 x a^{3} + 6 a^{3}

分解出因式

a^{3}

a^{3} (x^{2} - 5 x + 6)

= a^{3} (x^{2} - 5 x + 6) + (x^{2} - 5 x + 6)

因式分解出通项

(x^{2} - 5 x + 6) : (x^{2} - 5 x + 6) (a^{3} + 1)

= (x^{2} - 5 x + 6) (a^{3} + 1)

因式分解

x^{2} - 5 x + 6 : (x - 2) (x - 3)

= (x - 2) (x - 3) (a^{3} + 1)

因式分解

a^{3} + 1 : (a + 1) (a^{2} - a + 1)

= (x - 2) (x - 3) (a + 1) (a^{2} - a + 1)

s im pl i f y (8^{x})^{x} - 8^{x} - 3

f a c t or x^{2} - 3 x y

s im pl i f y \frac{x}{5} - \frac{( x - 2 )}{3} + x

s im pl i f y l (sin^{3} (t) - cos^{2} (t) + sin^{2} (t) + cos^{3} (t))

f a c t or 4 x^{4} - x^{2} - 16 x + 8