1. 6.3 Dividing polynomials

2. Divide using long division.
(x2 – 3x – 40) ÷ (x + 5)
(x3 + 3x2 – x + 2) ÷ (x – 1)
(9x3 – 18x2 – x + 2) ÷ (3x + 1)

3. The volume in cubic inches of the decorative box can be expressed as the product of the lengths of its sides as V(x) = x3 + x2 – 6x. Write linear expressions with integer coefficients for the locker’s length and height.

4. Divide using synthetic division.
(x3 + 3x2 – x – 3) ÷ (x – 1)
(x3 – 7x2 – 7x + 20) ÷ (x + 4)

5. (x3 + 27) ÷ (x + 3)
(x4 – 2x3 + x2 + x – 1) ÷ (x – 1)
(x4 – 5x2 + 4x +12) ÷ (x + 2)

6. Remainder Theorem Thm: If a polynomial P(x) of degree n ≥ 1 is divided by (x-a), where a is a constant, then the remainder is P(a).

7. Use synthetic division and the Remainder Theorem to find P(a).
P(x) = x3 – 7x2 + 15x – 9; a = 3
P(x) = x3 + 7x2 + 4x; a = -2

8. Determine whether each binomial is a factor of x3 + x2 – 16x – 16.