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Standard XII

Mathematics

Sum of Coefficients of All Terms

What is the d...

Question

What is the degree of $(x^{2} + 1)^{4} (x^{3} + 1)^{3}$ as a polynomial is $x$ ?

17

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Solution

The correct option is B $17$
$(x^{2} + 1)^{4} = x^{8} + 4 x^{4} + 1 + 4 x^{6} + 4 x^{2} + 2 x^{4}$
Term with Highest power in $(x^{2} + 1)^{4} = x^{8}$
$(x^{3} + 1)^{3} = x^{9} + 1 + 3 x^{6} + 3 x^{3}$
Term with highest power in $(x^{3} + 1)^{3} = x^{9}$
Term with highest power in $(x^{2} + 1)^{4} (x^{3} + 1)^{3} = x^{8} \times x^{9} = x^{17}$
Degree of $(x^{2} + 1)^{4} (x^{3} + 1)^{3} = 17$

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Similar questions

Q. The expression

(x + (x^{3} - 1)^{\frac{1}{2}})^{5} + (x - (x^{3} - 1)^{\frac{1}{2}})^{5}

is a polynomial of a degree :

Q. Express

{(x + \sqrt{x^{2} + 1})}^{3} + {(x - \sqrt{x^{2} + 1})}^{3}

as a polynomial in

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Q. What is the degree of the polynomial

16 x^{6} + 5 (x^{2})^{7} + 12 x - 33 x^{8} + 42 ?

Write the correct alternative answer for each of the following questions.

(i) Which of the following is a polynomial ?
(A)

\frac{x}{y}

(B)

x^{\sqrt{2}} - 3 x

(C)

x^{- 2} + 7

(D)

\sqrt{2} x^{2} + \frac{1}{2}

(ii) What is the degree of the polynomial

\sqrt{7}

?
(A)

\frac{1}{2}

(B) 5 (C) 2 (D) 0

(iii) What is the degree of the 0 polynomial ?

(A) 0 (B) 1 (C) undefined (D) any real number

(iv) What is the degree of the polynomial 2x²+ 5x³+ 7?
(A) 3 (B) 2 (C) 5 (D) 7

(v) What is the coefficient form of

x^{3} - 1

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(A) (1,

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1) (B) (3,

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1) (C) (1, 0, 0,

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1) (D) (1, 3,

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1)

(vi)

p (x) = x^{2} - 7 \sqrt{7} x + 3

then

p (7 \sqrt{7}) = ?

(A) 3 (B)

7 \sqrt{7}

(C)

42 \sqrt{7} + 3

(D)

49 \sqrt{7}

(vii) When

x = - 1

, what is the value of the polynomial 2x³+ 2x ?
(A) 4 (B) 2 (C)

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(D)

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(viii) If

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, what is a factor of the polynomial

3 x^{2} + m x

then find the value of m.
(A) 2 (B)

-

2 (C)

- 3

(D) 3

(ix) Multiply ( x²

-

3) (2x

-

7x³+ 4) and write the degree of the product.
(A) 5 (B) 3 (C) 2 (D) 0

(x) Which of the following is a linear polynomial ?

P (x) = {(\sqrt{x^{5} - 1} + x)}^{7} - {(\sqrt{x^{5} - 1} - x)}^{7}

is a polynomial of degree

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What is the degree of (x2+1)4(x3+1)3 as a polynomial is x?

The correct option is B 17(x2+1)4=x8+4x4+1+4x6+4x2+2x4Term with Highest power in (x2+1)4=x8(x3+1)3=x9+1+3x6+3x3Term with highest power in (x3+1)3=x9Term with highest power in (x2+1)4(x3+1)3=x8×x9=x17Degree of (x2+1)4(x3+1)3=17

What is the degree of $(x^{2} + 1)^{4} (x^{3} + 1)^{3}$ as a polynomial is $x$ ?