Question

Algebraic Expressione
9. 86- 15x - 716x - 9) - 2{10x-512 - 3x]}}
10. 12x - 3x +5x' - {7x-(4-3x - *°) +6x) - 3x1
11. 5a-la" - {2a(1 - a + 4a') - 3ala' - 5a - 31 - Ba
12. 3- (x - 2y - (5x +y - 3) + 2x) - (x - 3y)
13. xy - lyz - zx - {yx - (3y - x2) - (xy - zyl]
14. 2a - 3b - 13a - 2b - {a-c-la-2b)
16. -a -la + {a +-2a-la-2b)}- bl
16. 2a - [4b - {4a - (3b-2a + 2b)
17. 5x - 4y - {7x - (32-2y) + 4z -3(x + 3y - 2)​

Answer 1

Answer:

1. For polynomial 2x2 - 3x5 + 5x6.

We observe that the above polynomial has three terms. Here the first term is 2x2, the second term is -3x5 and the third term is 5x6.

Now we will determine the exponent of each term.

(i) the exponent of the first term 2x2 = 2

(ii) the exponent of the second term 3x5 = 5

(iii) the exponent of the third term 5x6 = 6

Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6.

Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6.

2. Find the degree of the polynomial 16 + 8x – 12x2 + 15x3 - x4.

We observe that the above polynomial has five terms. Here the first term is 16, the second term is 8x, the third term is – 12x2, the fourth term is 15x3 and the fifth term is - x4.

Now we will determine the exponent of each term.

(i) the exponent of the first term 16 = 0

(ii) the exponent of the second term 8x = 1

(iii) the exponent of the third term – 12x2 = 2

(iv) the exponent of the fourth term 15x3 = 3

(v) the exponent of the fifth term - x4 = 4

Since, the greatest exponent is 4, the degree of 16 + 8x – 12x2 + 15x3 - x4 is also 4.

Therefore, the degree of the polynomial 16 + 8x – 12x2 + 15x3 - x4 = 4.