Question

How do you factor completely: `21x^3 + 35x^2 + 9x + 15`?

Answer 1

Factor by grouping to find:

`21x^3+35x^2+9x+15=(7x^2+3)(3x+5)`

Explanation:

`21x^3+35x^2+9x+15`

`=(21x^3+35x^2)+(9x+15)`

`=7x^2(3x+5)+3(3x+5)`

`=(7x^2+3)(3x+5)`

The term `7x^2+3` has no linear factors with real coefficients since `7x^2+3 >= 3 > 0` for all `x in RR`.