OPERATIONS ON POLYNOMIALS WORKSHEET

1. Add : (5x2 + 4x + 1) + (2x2 + 5x + 2)

2. Subtract (2x2 + 2y2 - 6) from  (3x2 - 7y2 + 9).

3. Multiply : (3x3)(6x4)

4. Multiply using distributive property : (x + 3)(x - 6)

5. Multiply using FOIL method : (x + 4)(x + 5)

6. Multiply : 5(3x2 + 5x + 7)

7. Multiply : (x + 3)(x2 - 5x + 7)

8. Divide (x3 - 4x2 + 6x) by x, where x  0.

9. Divide (x2 - 9) by (x - 3), where x  3.

10. Find the quotient and the remainder when the polynomial (5x2 - 7x + 2) is divided by (x - 1), using long division. 

1. Answer :

Associative and Commutative Properties can be used to regroup the like terms together and combine them as shown below.  

= (5x2 + 4x + 1) + (2x2 + 5x + 2)

= (5x2 + 2x2) + (4x + 5x) + (1 + 2)

= 7x2 + 9x + 3

2. Answer : 

= (3x2 - 7y2 + 9) - (2x2 + 2y2 - 6)

Distributive Property. 

= 3x2 - 7y2 + 9 - 2x2 - 2y2 + 6

Group like terms together. 

= (3x2 - 2x2) + (-7y- 2y2) + (9 + 6)

Combine like terms. 

= x2 - 9y2 + 15

3. Answer :

(3x3)(6x4)

Group factors with like bases together. 

= (3 ⋅ 6)(x3 ⋅ x4)

Use the Product of Powers Property. 

= 18x3 + 4

= 18x7

4. Answer : 

(x + 3)(x - 6)

Distribute. 

x(x - 6) + 3(x - 6)

Distribute again. 

x(x) + x(-6) + 3(x) + 3(-6)

Multiply. 

= x2 - 6x + 3x - 18

Combine like terms. 

= x2 - 3x - 18

5. Answer : 

Multiply the First terms :

(x + 4)(x + 5) ---> ⋅ = x2

Multiply the Outer terms :

(x + 4)(x + 5) ---> x ⋅ 5 = 5x

Multiply the Inner terms :

(x + 4)(x + 5) ---> 4 ⋅ x = 4x

Multiply the Last terms :

(x + 4)(x + 5) ---> 4 ⋅ 5 = 20

(x + 4)(x + 5) = x5x 4x 20

(x + 4)(x + 5) = x+ 9x + 20

6. Answer : 

= 5(3x2 + 5x + 7)

Distribute 2.

= 5(3x2) + 5(5x) + 5(7)

Multiply. 

= 15x2 + 25x + 35

7. Answer :

= (x + 3)(x2 - 5x + 7)

Distributive. 

= x(x2 - 5x + 7) + 3(x2 - 5x + 7)

Distribute again. 

= x(x2) + x(-5x) + x(7) + 3(x2) + 3(-5x) + 3(7)

Simplify. 

= x3 - 5x2 + 7x + 3x2 - 15x + 21

Combine the like terms.

= x3 - 5x2  + 3x2+ 7x - 15x + 21

= x3 - 2x2 - 8x + 21

8. Answer : 

= (x3 - 4x2 + 6x)/x

x3/x - 4x2/x + 6x/x

= x2 - 4x + 6

9. Answer : 

= (x2 - 9)/(x - 3)

= (x2 - 32)/(x - 3)

Using the algebraic identity a2 - b2 = (a + b)(a - b) to factor (x2 - 32). 

= [(x + 3)(x - 3)]/(x - 3)

= x + 3

10. Answer : 

Quotient = 5x - 2

Remainder = 0

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