Polynomial Exercises

1.In each following identities, find the values of A, B, C, D, and R! (if any)

a. x³ – x² – 2x + 12 ≡ (x+2)(Ax² + Bx + C) +R

b. 12x³ + 11x² – 7x + 5 ≡ (3x+2)(Ax² + Bx + C) +R

c. 9x³ + 12x² – 15x + 10 ≡ (3x+4)(Ax² + Bx + C) +R

d. 6x⁴ – 5x³ – x² + 3x + 2  ≡ (3x+4)(Ax³ + Bx² + Cx + D) +R

 

2. Find the quotient and the remainder when: [Hint : quotient=Q(x), remainder=S(x)]

a. 3x³ – 2x² – x + 4 is divided by x+2

b. x⁴ – x³ + 3x² + x + 2 is divided by x-1

c. 2x⁵ + x⁴ + 3x³ + 2x² + 4x – 6  is divided by x² – 3x + 4

d. x⁵ – 3x⁴ + 4x³ – x² + 4x + 2  is divided by x³ – 4x² – 1

 

3. When x³ + 2x² – px + 1 is divided by x-1 the remainder is 5. Find the value of p.

4. When 2x³  – x²  + ax + b is divided by x-2 the remainder is 25. When divided by x-2 the remainder is 25. When divided by x+1 the remainder is -5. Find the value of a and b.

5. The polynomial F(x) leaves a remainder of 12 when divided by x-1, 4 when divided by x+1, and 16 when divided by x-3. Find the remainder when F(x) is divided by (x²-1)(x-3).

6.  x⁴ – 7x³  + px² + qx – 16 is exactly divisible by x² – 4x + 4. Find the values of p and q, hence find the quotient.

7. Find the remainder when the expression 1/45(8x³¹  – x³³  – 128x²⁶) – 3(x⁴  – 5x²) is divided by x²  – x – 2.

 

Tune in for the answers!