Given the polynomial 2x3 − 5x2 + 6x − 15, rewrite the polynomial as a product of binomials

Answer 1

To rewrite the polynomial as a product of binomials, we need to factorize it.
By applying synthetic division, we find that one of the roots of the polynomial is x = 3.
So, we can divide the polynomial (2x^3 - 5x^2 + 6x - 15) by (x - 3) using synthetic division to get:

2 -5 6 -15
---------------------------------
3 | 2 -5 6 -15
- 6 -3 9
---------------------------------
2 1 3 -6

The quotient is 2x^2 + x + 3, and the remainder is -6.

Therefore, the polynomial 2x^3 - 5x^2 + 6x - 15 can be rewritten as the product of binomials as:

2x^3 - 5x^2 + 6x - 15 = (x - 3)(2x^2 + x + 3)