Question

The binomial x + 3 is one factor of 2x3 - x2 - 18x + 9. Use complete sentences to explain how you use (either) polynomial division or synthetic division to find the remaining factors. List the remaining factors.

Answer 1

2x3-x2-18x+9
= 2x(x2-9)-1(x2-9)
= (2x-1)(x2-9)

= (2x-1)(x-3)(x+3)

Answer 2

could you explain it a little bit more, i dont really understand this.

Answer 3

To reduce the problem to one of factoring a quadratic, divide the original cubic (2x3-x2-18x+9) by the given linear factor (x+3) using either synthetic division or polynomial long division.

Answer 4

The resulting quadratic (2x2-7x+3) can be factored directly or by its roots found using the quadratic formula. The roots (r1, r2) can be turned into factors by eliminating fractions from the product 2(x-r1)(x-r2).

The remaining factors are (2x-1), (x-3).

So your final answer will be 2x3-x2-18x+9 = (x+3)(2x-1)(x-3)