因式分解 a^3+a^2-21a-45

解答

因式分解

a^{3} + a^{2} - 21 a - 45

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

求解步骤

a^{3} + a^{2} - 21 a - 45

使用有理根定理

= (a + 3) \frac{a ^{3} + a ^{2} - 21 a - 45}{a + 3}

\frac{a ^{3} + a ^{2} - 21 a - 45}{a + 3} = a^{2} - 2 a - 15

= (a + 3) (a^{2} - 2 a - 15)

因式分解

a^{2} - 2 a - 15 : (a + 3) (a - 5)

= (a + 3) (a + 3) (a - 5)

使用指数法则:

aa = a^{2}

(a + 3) (a + 3) = (a + 3)^{2}

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

f a c t or 1 - 125 y^{3}

f a c t or p^{3} + 9 p^{2} + 27 p + 27

f a c t or 32 p^{4} + 72 p^{2} q^{2} + 162 q^{4}

s im pl i f y l (cos^{22} (t))

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