Verified answer

(2x^2 - 5x - 3)/(x - 3)

= (2x^2 + x - 6x - 3)/(x - 3)

= [(2x^2 + x) - (6x + 3)]/(x - 3)

= [x(2x + 1) - 3(2x + 1)]/(x - 3)

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

= 2x + 1

(2x^2 - 5x - 3)/(x - 3)

Find the factors such that the product of the factors is the trinomial

2x^2 - 5 - 3

This can be done by trial and error and checked using the FOIL method of simplifying polynomials.

(2x + 1) (x - 3)

Multiply using the FOIL method to confirm (check and test).

2x x x = 2x^2

2x x -3 = -6x

1 x x = 1x

1 x -3 = -3

2x^2 - 6x + 1x - 3

2x^2 - 5x - 3

Therefore:

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

Reduce the expression by cancelling out the common factor of (x - 3) from the numerator and denominator.

(2x + 1)

Remove the parentheses around the expression 2x + 1.

The answer is:

2x + 1

(X-3)/(2X^2-5X-3)

answer: (-2X-1)

To check your work:

If you multiply (-2X-1)(X-3)= -2X^2+5X=3

Then multiply by -1 and that will give you (2X^2-5X-3) which was what you were were trying to simplify

2x+1.

(2x+1)(x-3)=2x^2-6x+x-3

=2x^2-5x-3