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Which of the following gives the correct factors of \( \Large 4x^{2}- \left(x^{2}-3\right)^{2} \)?
I. \( \Large \left(x-2\right) \left(x-1\right) \)
II. \( \Large \left(x-1\right) \left(x+3\right) \)
III. \( \Large \left(3-x\right) \left(x+1\right) \)
IV. \( \Large \left(2x-1\right) \left(2x+3\right) \)
Select the correct answers from the codes given below :

A) I and III
B) II and IV
C) II and III
D) I, II and III

Correct Answer:



C) II and III

Description for Correct answer:
\( \Large 4x^{2}- \left(x^{2}-3\right)^{2} = \left(2x\right)^{2}- \left(x^{2}-3\right)^{2} \)

= \( \Large \left(2x+x^{2}-3\right) \left(2x-x^{2}+3\right) \)

= \( \Large \left(x^{2}+2x-3\right) \left(2x-x^{2}+3\right) \)

= \( \Large \left(x+3\right) \left(x-1\right) \left(3-x\right) \left(x+1\right) \)

Part of solved Polynomials questions and answers : >> Elementary Mathematics >> Polynomials

Comments

Similar Questions

1). The remainder when \( \Large 2x^{3}-3x^{2}+4x-1 \) is divided by x - 1 is

A). -10

B). 2

C). 1

D). 10

2). If \( \Large x+\frac{1}{x}=\sqrt{3} \), then \( \Large x^{3}+\frac{1}{x^{3}} \) is equal to

A). 0

B). 1

C). 3

D). \( \Large \left(x+1\right) \)

3). One of the factors of \( \Large x^{3}+6x^{2}+11x+6 \) is

A). \( \Large \left(x-\frac{1}{2}\right) \)

B). \( \Large \left(x+\frac{1}{2}\right) \)

C). \( \Large \left(x-1\right) \)

D). \( \Large \left(x+1\right) \)

4). If polynomial \( \Large x^{3}-3x^{2}+kx+42 \) is divisible by \( \Large x+3 \), then value of k will be

A). 4

B). 14

C). -4

D). -14

5). H.C.F. and L.C.M. of polynomials \( \Large \left(x-2\right) \), \( \Large x^{2}-4 \) are respectively

A). 1, \( \Large x - 2 \)

B). \( \Large x - 2 \), 8

C). \( \Large x - 2 \), \( \Large x + 2 \)

D). \( \Large x - 2 \), \( \Large x^{2}-4 \)

6). If \( \Large a+b+c=0 \), thena \( \Large a^{3}+b^{3}+c^{3} \) is equal to

A). \( \Large a^{2} \left(b+c\right)+b^{2} \left(c+a\right)+c^{2} \left(a+b\right) \)

B). \( \Large 3 \left(b+c\right) \left(c+a\right) \left(a+b\right) \)

C). \( \Large 3 abc \)

D). \( \Large 6 a^{2}b^{2}c^{2} \)

7). If \( \Large a^{m^{n}}= \left(a^{m}\right)^{n} \), then the value of m is

A). n

B). \( \Large \frac{n}{n^{n-1}} \)

C). \( \Large \frac{1}{n^{n-1}} \)

D). \( \Large n^{\frac{n-1}{n}} \)

8). Value of \( \Large \left(X^{b-c}\right)^{b+c},\ \left(X^{c-a}\right)^{c+a},\ \left(X^{a-b}\right)^{a+b} \) is

A). 0

B). X

C). 1

D). X+1

9). If \( \Large 2^{x}=4^{y}=8^{z} and \frac{1}{2x}+\frac{1}{4y}+\frac{1}{6z}=\frac{24}{7} \), then value of z is

A). \( \Large \frac{7}{16} \)

B). \( \Large \frac{7}{32} \)

C). \( \Large \frac{7}{48} \)

D). \( \Large \frac{7}{46} \)

10). Which one of the following is a polynomial?

A). \( \Large x^{3}+\sqrt{3x^{2}}+4\sqrt{x} \)

B). \( \Large x^{6}+2\sqrt{x^{2}}+x^{-1} \)

C). \( \Large x^{5}+x^{4}+x^{-1}+x^{-5} \)

D). \( \Large x^{3}+\sqrt{5x^{2}}+x+\sqrt{3} \)