Topics

H.C.F. of the polynomials \( \Large x^{2}+3x+2 \) and \( \Large x^{3}+3x^{2}+3x+1 \) using Euclidean algorithm is


A) \( \Large x+4 \)

B) \( \Large 3x+2 \)

C) \( \Large 2x+1 \)

D) \( \Large x+1 \)

Correct Answer:
D) \( \Large x+1 \)

Description for Correct answer:
\( \Large x^{2}+3x+2 = \left(x+1\right) \left(x+2\right) \)

\( \Large x^{3}+3x^{2}+3x+1 = x^{3}+x^{2}+2x^{2}+2x+x+1 \)

= \( \Large x^{2} \left(x+1\right)+2x \left(x+1\right)+1 \left(x+1\right) \)

= \( \Large \left(x+1\right) \left(x^{2}+2x+1\right) \)

Therefore, \( \Large HCF = x+1 \)

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




Comments
No comments available




Similar Questions
1). Let I, m and n be real dividing such that \( \Large l + m \ne n \). What is the quotient on dividing \( \Large l^{3}-m^{3}+n^{3}+3lmn \) by \( \Large \left(l-m+n\right) \)?
A). \( \Large l^{2}+m^{2}+n^{2}-lm-mn-ln \)
B). \( \Large l^{2}+m^{2}+n^{2}+lm+mn-ln \)
C). \( \Large l^{2}+m^{2}+n^{2}+lm+mn+ln \)
D). \( \Large l^{2}-m^{2}+n^{2}-lm-mn+ln \)
-- View Answer
2). What is the. remainder when \( \Large x^{4}+1 \) is divided \( \Large x-2 \)?
A). 17
B). 15
C). 7
D). 1
-- View Answer
3). If \( \Large x+y+z=0 \) and \( \Large xyz \ne 0 \), then what is the value of \( \Large \frac{1}{x^{2}+y^{2}-z^{2}}+\frac{1}{y^{2}+z^{2}-x^{2}}+\frac{1}{z^{2}+x^{2}-y^{2}} \)
A). 0
B). 1
C). -1
D). \( \Large \frac{1}{2} \)
-- View Answer
4). For what value of p, is the coefficient of \( \Large x^{2} \) in the product \( \Large \left(2x-1\right) \left(x-k\right) \left(px+1\right) \) equal to 0 and the constant term equal to 2?
A). 2
B). \( \Large \frac{2}{5} \)
C). \( \Large \frac{5}{2} \)
D). 5
-- View Answer
5). If m and n are natural numbers such that \( \Large 2^{m}-2^{n}=960 \), then what is the value of m?
A). 10
B). 12
C). 16
D). Cannot be determined
-- View Answer


6). When \( \Large x^{3}+2x^{2}+4x+b \) is divided by \( \Large x+1 \), the quotient is \( \Large x^{2}+ax+3 \) and remainder is \( \Large -3 +2b \). What are the values of a and b respectively?
A). 1, 0
B). 0,1
C). 1, 1
D). -1, -1
-- View Answer
7). If \( \Large y+\frac{1}{z}=1\ and\ x+\frac{1}{y}=1 \), then what is the value of xyz?
A). 1
B). -1
C). 0
D). \( \Large \frac{1}{2} \)
-- View Answer
8). What are the values of A and B respectively, if \( \Large \frac{\sqrt{5}-1}{\sqrt{5}+1}+\frac{\sqrt{5}+1}{\sqrt{5}-1} = A+B\sqrt{5}? \)
A). 3, 0
B). 0, 3
C). 0. 0
D). 3, 3
-- View Answer
9). If \( \Large x^{4}+y^{4}=17\ and\ x+y=1 \), then what is the value of \( \Large x^{2}y^{2}-2xy \)?
A). 8
B). 10
C). 12
D). 16
-- View Answer
10). If \( \Large \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c} \), where \( \Large a+b+c \ne 0 \), \( \Large abc \ne 0 \), then what is the value of \( \Large \left(a+b\right) \left(b+c\right) \left(c+a\right)? \)
A). 0
B). 1
C). -1
D). 2
-- View Answer
Home About Us Terms and Conditions Privacy Policy Contact us