Fill in the blanks. Give what is asked. 1. A short method of dividing polynomial expressions using only the coefficient of the terms is called 2. If the polynomial P(x) is divided by (x - c) the remainder R is a constant and is equal to P(c) is called 3. x + 5 is a factor of f(x) if and only if f(-5) = 4. The degree of the polynomial equation 2x3 + x2 - x + 1 = 0 is 5. Is x - 2 a factor of x3 - 8? 6. If 5x3 + 3x - 8 is divided by x - 1 using synthetic division, the numbers in the first row should be 7. If x3 - 4x2 + 2x - 5 is divided by x - 3, the remainder is To answer # 8 - 10 refer to the synthetic division below 2 1 -23 20 -8 28 -20 2 -7 5 0 Express each item asked as a polynomial in x 8. Dividend: 9. Divisor: 10. Quotient: I1. Read and analyze each problem carefully. Solve what is asked. Show solution. (2 points each) 1. Find the remainder when P(x) = x3 + 5x - 7 is divided by x + 1 2. Show that x - 2 is a factor of x3 + 7x2 + 2x - 40. 3. Find the quotient and remainder of 2x* - 18x2- 7 - x3 when divided by x - 3. 4. Find k if 2x3 + 3x2 + kx - 2 leaves a remainder 3 when divided by x + 1. 5. Find k such that x + 2 is a factor of 2x3 + x2 - kx - 6