What is factor a^5-6a^4+16a^3-32a^2+48a-32 ?

The solution to factor a^5-6a^4+16a^3-32a^2+48a-32 is (a-2)^3(a^2+4)

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factor a^5-6a^4+16a^3-32a^2+48a-32

factor

a^{5} - 6 a^{4} + 16 a^{3} - 32 a^{2} + 48 a - 32

(a - 2)^{3} (a^{2} + 4)

Solution steps

a^{5} - 6 a^{4} + 16 a^{3} - 32 a^{2} + 48 a - 32

Use the rational root theorem

= (a - 2) \frac{a ^{5} - 6 a ^{4} + 16 a ^{3} - 32 a ^{2} + 48 a - 32}{a - 2}

\frac{a ^{5} - 6 a ^{4} + 16 a ^{3} - 32 a ^{2} + 48 a - 32}{a - 2} = a^{4} - 4 a^{3} + 8 a^{2} - 16 a + 16

= (a - 2) (a^{4} - 4 a^{3} + 8 a^{2} - 16 a + 16)

Factor

a^{4} - 4 a^{3} + 8 a^{2} - 16 a + 16 : (a - 2) (a - 2) (a^{2} + 4)

= (a - 2) (a - 2) (a - 2) (a^{2} + 4)

Apply exponent rule:

aaa = a^{3}

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

= (a - 2)^{3} (a^{2} + 4)

1.25 \cdot 14.9 + 0.75 \cdot 1.1 + 14.9 \cdot 0.75 + 1.1 \cdot 1.25

0.5 (8 \cdot 1 0^{5})

18 x^{3} + 30 x^{2} + 3 x + 5

4 a^{2} = 32 a

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What is factor a^5-6a^4+16a^3-32a^2+48a-32 ?
The solution to factor a^5-6a^4+16a^3-32a^2+48a-32 is (a-2)^3(a^2+4)