# Which of the following is a factor of 5x^{3} + 320?

5, x + 4, x2 - 4x + 16, All of the above

**Solution:**

5x^{3} + 320 can be simplified as follows:

5x^{3} + 5(64)

= 5(x^{3} + 64)

= 5(x^{3} + 43 )

x^{3} + 4^{3} is of the form a^{3} + b^{3} .

Since we know this algebraic identity,

a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})

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

= (x + 4)(x^{2} - 4x + 16)

Therefore

5(x^{3} + 64) = 5(x + 4)(x^{2} - 4x + 16)

The factors are 5, (x + 4) and (x^{2} - 4x + 16)

## Which of the following is a factor of 5x^{3} + 320?

**Summary:**

The factors of 5x^{3} + 320 are 5, x + 4, x^{2} - 4x + 16 i.e. all of the above.

Math worksheets and

visual curriculum

visual curriculum