Question

One of the factor of a^3 + 64 is a +4. The other factor is

Answer 1

Answer : a^2 - 4a + 16

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Answer 2

Given : one of the factor of (a³ + 64) is (a + 4).

To find : The other factor of (a³ + 64) is...

Solution : This can be solved by two methods.

long division method :

a + 4) a³ + 64 (a² - 4a + 16

a³ + 4a²

....,...........................

-4a² + 64

-4a² - 16a

............................

16a + 64

16a + 64

..........................

0

therefore the other factor of (a³ + 64) is (a² - 4a + 16).

applying Algebraic formula,

you know, a³ + b³ = (a + b)(a² - ab + b²)

so, (a³ + 64) = (a³ + 4³) = (a + 4)(a² - 4a + 4²)

= (a + 4)(a² - 4a + 16)

here it is clear that (a + 4) and (a² - 4a + 16) are two factors of (a³ + 64). now if (a + 4) is a factor then the other factor of (a³ + 64) is (a² - 4a + 16).