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)(Ax+ Bx + C) +R

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

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

d. 6x4 – 5x– x2 + 3x + 2  ≡ (3x+4)(Ax3 + Bx+ 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 – x+ 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!

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