1 Simplify x^2 +4x+3 / x+3
2 simplify x^2 -1 / x+1
3 Divide x^2 - 1 into f(x) = 2x^3 + 3x^2 + 9x + 5. Write your answer in the form given by the Division Algorithm; in other words, write your answer as: 2x^3 + 3x^2 + 9x + 5 = q(x)(x^2 - 1) + r(x) for some polynomials q(x) and r(x).
4. Factor the expression x^3 + 8y^3
1. Well, for the first one, you can factor the numerator so that it is of the form: (x+3)(x+1). Use FOIL to verify this for reinforcement. What do you get when you divide this by the denominator.
2. The second one has a numerator which is the difference of squares. It is of the form (a + b)(a - b). When you write it of this form you get cancellations in the numerator and denominator.
4. For the last one, this is the sum of 2 cubes. It is written of the form:
(a + b)*(a^2 - ab + b^2). Use FOIL to verify this and then make an attempt to do it for the one above. To find a and b, take the cube root of each term. (What is the cube root of x^3? What is the cube root of 8*y^3?) Then, you just need to find the a^2 and b^2 values to substitute into the above form.