Operations on polynomials

(the database of solved problems)

All the problems and solutions shown below were generated using the Polynomial Operations Calculator.

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ID	Problem	Count
1	Multiply polynomial $6 x^{2} + 2 x$ by $- 9 x^{2} - 10 x$ .	441
2	Add $2 a + 5$ and $4 a - 3$ .	222
3	Add $5 + 7 x^{3} + 3 x^{2}$ and $- 12 + 5 x + 6 x^{2}$ .	208
4	Subtract polynomials: $3 q^{4} + 3 q^{3} + 7 q^{2} + q + 9$ , $3 q^{4} + q^{3} + 5 q^{2} + q + 7$ .	206
5	Multiply polynomial $y^{2} + 2 y$ by $y^{2} + 5 y + 8$ .	199
6	Multiply polynomial $5 a + 2$ by $2 a - 3$ .	196
7	Multiply polynomial $2 x - 5$ by $x - 5$ .	187
8	Add $- 3 a^{3} - 4 a^{2} - 9 a$ and $- 8 a^{3} - 9 a + 5$ .	172
9	Subtract polynomials: $2 x^{2} + x - 3$ , $x^{2} - 3 x + 5$ .	165
10	Add $2 x^{3} - 2 x - 3$ and $2 x + 5$ .	153
11	Add $5 p^{2} - 3$ and $2 p^{2} - 3 p^{3}$ .	149
12	Add $x$ and $2 x + 5$ .	146
13	Subtract polynomials: $3 a - 4 a$ , $6 a - 12 a$ .	130
14	Subtract polynomials: $4 r^{2} - 4 r - 8$ , $9 r^{3} - 5 r^{2} - 9 r + 7$ .	110
15	Subtract polynomials: $5 x^{2} - 9 x - 10$ , $- 6 x^{2} + 6 x$ .	108
16	Add $10 a$ and $4 a - 3$ .	106
17	Add $- q + 4$ and $7 q^{3} - 4 q^{2} + 8 q + 5$ .	104
18	Subtract polynomials: $2 x^{3} - 3$ , $x^{2} - 15 x$ .	104
19	Add $3 x^{2} - x + 1$ and $15 - 9 x - 2 x^{2}$ .	97
20	Subtract polynomials: $7 b^{2} + 6 b - 7$ , $4 b^{2} - 2$ .	89
21	Multiply polynomial $10 a$ by $2 a - 3$ .	84
22	Add $- 4 x^{2} + 4 x$ and $- 6 x^{2} - 8$ .	65
23	Multiply polynomial $6 x^{2} + 3 x + 1$ by $- 19 x^{2} - 2$ .	61
24	Subtract polynomials: $5 x^{2} - 9 x - 10$ , $- 6 x^{2} + 6 x$ .	59
25	Multiply polynomial $- 4 x^{2} - 5 x - 1$ by $4 x^{2} - 6 x - 2$ .	59
26	Subtract polynomials: $7 f^{2} - f$ , $- 4 f + 5$ .	53
27	Subtract polynomials: $- 12 x + x - 6$ , $8 x - 6 x - 4$ .	52
28	Subtract polynomials: $x^{2} + 8 x$ , $- 3 x^{2} - 3 x - 7$ .	50
29	Add $3 x - 4$ and $5 + 3 x - 4 x^{2}$ .	49
30	Multiply polynomial $2 x^{3} - 2 x - 3$ by $2 x + 5$ .	45
31	Multiply polynomial $2 x$ by $3 x^{2} - 4 x$ .	43
32	Multiply polynomial $3 x - 2$ by $5 x + 1$ .	41
33	Multiply polynomial $x^{2} - x + 3$ by $2 x^{2} + 4 x - 3$ .	41
34	Add $- 4 x^{2} - 5 x - 1$ and $4 x^{2} - 6 x - 2$ .	37
35	Subtract polynomials: $8 x^{3} - 10 x^{2} + 30$ , $4 x^{3} - 7 x^{2} - 6$ .	37
36	Add $7 x^{2} + x + 1$ and $6 x^{2} - 8 x - 10$ .	36
37	Subtract polynomials: $- 8 n^{4} + n^{3} - n^{2} - n - 2$ , $- 2 n^{4} + 5 n^{3} - 6 n^{2}$ .	36
38	Add $7 x^{3} + 4 x^{2} + 3 x + 12$ and $9 x^{3} - 2 x^{2} + 5 x - 8$ .	34
39	Multiply polynomial $4 x - 3$ by $x + 6$ .	33
40	Subtract polynomials: $10 x^{2} - 4 + 3$ , $7 x^{2} - 3 x + 13$ .	31
41	Subtract polynomials: $3 u^{2}$ , $- 15 u$ .	31
42	Multiply polynomial $10 x^{2} - 4 + 3$ by $7 x^{2} - 3 x + 13$ .	30
43	Subtract polynomials: $3 q^{2} + 5 q$ , $6 q^{2} + 8 q + 9$ .	30
44	Multiply polynomial $3 x - 2$ by $3 x + 4$ .	30
45	Multiply polynomial $2 x + 3$ by $5 x - 3$ .	29
46	Multiply polynomial $2 y^{2}$ by $5 y^{2} - 5 y + 2$ .	28
47	Multiply polynomial $6 c^{5} - 2 c^{4} - 2$ by $- 11 c^{2} - 15$ .	28
48	Subtract polynomials: $9 q^{4} + 2 q^{2} - 4$ , $q^{3} + 8 q^{2} - 5$ .	27
49	Add $3 x - 4$ and $5 + 3 x - 4 x$ .	27
50	Add $6 + 7 q^{3} - 3 q^{4}$ and $9 q^{4} + 2 q^{2} - 4$ .	27