Question

(a) 1. Find the degree of the polynomial x2(3x4 + 7x - 5). If degree of flr) = 36 and degree of g(x) = 20 then fin -​

Answer 1

Answer:

Examples of polynomials and its degree:

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.

Step-by-step explanation:

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.

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Answer 2

Step-by-step explanation:

Find the value of k, if (x−2) is a factor of 4x

3

+3x

2

−4x+k.

Easy

View solution

>

On dividing x

5

−4x

3

+x

2

+3x+1 by polynomial g(x), the quotient and remainder are (x

2

−1) and 2 respectively. Find g(x).