Which of the following is a factor of 5x³ + 320?
5, x + 4, x2 - 4x + 16, All of the above

Solution:

5x³ + 320 can be simplified as follows:

5x³ + 5(64)

= 5(x³ + 64)

= 5(x³ + 43 )

x³ + 4³ is of the form a³ + b³ .

Since we know this algebraic identity,

a³ + b³ = (a + b)(a² - ab + b²)

x³ + 4³ = (x + 4)(x² - (4)(x) + 4²)

= (x + 4)(x² - 4x + 16)

Therefore

5(x³ + 64) = 5(x + 4)(x² - 4x + 16)

The factors are 5, (x + 4) and (x² - 4x + 16)

Which of the following is a factor of 5x³ + 320?

Summary:

The factors of 5x³ + 320 are 5, x + 4, x² - 4x + 16 i.e. all of the above.