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339 questions tagged with definition-polynomial.
Which is the correct identification of (p(x)=2x-2-5)?
B. द्विघात द्विपदीQuadratic binomial
इसकी घात (2) है और इसमें दो पद हैं। इसलिए यह द्विघात द्विपदी है। / Its degree is (2) and it has two terms. Therefore, it is a quadratic binomial.
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Which expression is a polynomial in (x) and does not have an \(x^2\) term?
A. \(x^4+3x-5\)
बहुपद में हर घात का पद होना जरूरी नहीं है। \(x^4+3x-5\) में उपस्थित घातें मान्य हैं। / A polynomial need not contain every power term. In \(x^4+3x-5\), the present powers are valid.
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If the highest power of a polynomial is (3), what is it called?
D. घन बहुपदCubic polynomial
सबसे बड़ी घात (3) होने पर बहुपद घन कहलाता है। बहुपद का प्रकार घात से पहचानें। / A polynomial with highest power (3) is called cubic. Identify the type of polynomial from its degree.
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Which expression is not a polynomial in (x) because (x) is in the denominator?
C. \(\frac{x+4}{x}\)
\(\frac{x+4}{x}=1+\frac{4}{x}\) है और \(\frac{4}{x}=4x^{-1}\) है। ऋणात्मक घात के कारण यह बहुपद नहीं है। / \(\frac{x+4}{x}=1+\frac{4}{x}\) and \(\frac{4}{x}=4x^{-1}\). Due to the negative power, it is not a polynomial.
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Which expression is a polynomial but not of degree (2)?
B. \(6x^4-x+3\)
\(6x^4-x+3\) बहुपद है और इसकी घात (4) है। इसलिए इसकी घात (2) नहीं है। / \(6x^4-x+3\) is a polynomial and its degree is (4). Therefore, it is not of degree (2).
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Which powers are present in \(x^5+2x^3-7\)?
A. (5), (3), (0)
\(x^5\) की घात (5), \(2x^3\) की घात (3), और स्थिर पद की घात (0) मानी जाती है। / The power of \(x^5\) is (5), the power of \(2x^3\) is (3), and the constant term is treated as power (0).
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Which option correctly identifies \(x^2-6x+9\)?
B. द्विघात त्रिपदी बहुपदQuadratic trinomial polynomial
इसकी घात (2) है और इसमें तीन पद हैं। इसलिए यह द्विघात त्रिपदी बहुपद है। / Its degree is (2) and it has three terms. Therefore, it is a quadratic trinomial polynomial.
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Which expression is not a polynomial in (x) but has a constant term?
C. \(x^{-4}+8\)
\(x^{-4}\) की घात ऋणात्मक है इसलिए यह बहुपद नहीं है। (8) केवल स्थिर पद है। / The power in \(x^{-4}\) is negative, so it is not a polynomial. (8) is only a constant term.
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What is the degree of \(4x^3+0x^5-6x+2\)?
B. (3)
\(0x^5\) शून्य पद है और घात तय नहीं करता। सबसे बड़ी अशून्य घात (3) है। / \(0x^5\) is a zero term and does not determine the degree. The highest non-zero power is (3).
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Why is \(x^3+x^{2/5}+1\) not a polynomial?
C. क्योंकि (x^{25}) की घात पूर्णांक नहीं है / Because the power in \(x^{2 / 5}\) is not an integer
बहुपद में चर की घातें पूर्णांक होनी चाहिए। \(x^{2/5}\) की घात \(\frac{2}{5}\) है, जो पूर्णांक नहीं है। / In a polynomial, powers of the variable must be integers. The power in \(x^{2/5}\) is \(\frac{2}{5}\), which is not an integer.
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Which option correctly states the main condition of a polynomial?
B. चर की घातें शून्य या धनात्मक पूर्णांक होंPowers of the variable are zero or positive integers
बहुपद में चर की घातें शून्य या धनात्मक पूर्णांक होनी चाहिए। यही परिभाषा की सबसे जरूरी शर्त है। / In a polynomial, powers of the variable must be zero or positive integers. This is the most important condition in the definition.
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In (p(x)=7x-5-2x+4), the \(x^4\), \(x^3\), and \(x^2\) terms are missing. What is its degree?
D. (5)
गायब पद घात को नहीं बदलते। सबसे बड़ी उपस्थित घात (5) है। / Missing terms do not change the degree. The highest present power is (5).
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How many terms are there in the polynomial \(x^4-3x^2+2x-11\)?
B. (4)
इसमें \(x^4\), \(-3x^2\), (2x) और (-11) चार पद हैं। पदों को चिन्ह सहित गिनें। / It has four terms: \(x^4\), \(-3x^2\), (2x), and (-11). Count terms with their signs.
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Which expression is a polynomial even though it has a fractional coefficient?
A. \(3x^2+\frac{5}{8}x-2\)
भिन्न गुणांक बहुपद में मान्य होते हैं। यहाँ (x) की घातें (2), (1) और (0) हैं। / Fractional coefficients are allowed in polynomials. Here the powers of (x) are (2), (1), and (0).
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In \(9x^0+4x\), \(x^0\) is considered equal to what?
D. (1)
\(x^0=1\) माना जाता है जब \(x\neq0\)। इसलिए \(9x^0\) स्थिर पद की तरह काम करता है। / \(x^0=1\) when \(x\neq0\). So \(9x^0\) acts like a constant term.
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Which statement is correct about the degree of the zero polynomial (0)?
B. इसकी घात परिभाषित नहीं होतीIts degree is not defined
(0) शून्य बहुपद है लेकिन उसकी घात परिभाषित नहीं होती। इसे शून्य से अलग स्थिर बहुपद से अलग रखें। / (0) is the zero polynomial but its degree is not defined. Keep it separate from a non-zero constant polynomial.
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Which expression is a linear polynomial in (t)?
D. (5t-9)
रैखिक बहुपद की घात (1) होती है। (5t-9) में सबसे बड़ी घात (1) है। / A linear polynomial has degree (1). In (5t-9), the highest power is (1).
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What type of polynomial is (23) considered?
A. स्थिर बहुपदConstant polynomial
(23) में कोई चर नहीं है इसलिए यह स्थिर बहुपद है। शून्य से अलग स्थिर बहुपद की घात (0) होती है। / (23) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
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What is the degree of the polynomial \(6x^7-4x^3+x-8\)?
C. (7)
बहुपद की घात सबसे बड़ी चर-घात होती है। यहाँ सबसे बड़ी घात (7) है। / The degree of a polynomial is the highest power of the variable. Here the highest power is (7).
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Which expression is not a polynomial in (x) because the variable has a negative power?
D. \(5x^{-3}+1\)
\(x^{-3}\) की घात ऋणात्मक है। बहुपद में ऋणात्मक घात स्वीकार्य नहीं होती। / The power in \(x^{-3}\) is negative. Negative powers are not allowed in a polynomial.
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If (p(x)=\(a^2-4\)x-4+(a+2)x-3+5x+1) has degree exactly (3), what is the value of (a)?
B. (2)
घात (3) के लिए \(x^4\) का गुणांक शून्य और \(x^3\) का गुणांक अशून्य होना चाहिए। (a=2) पर \(a^2-4=0\) और (a+2=4) है। / For degree (3), the \(x^4\) coefficient must be zero and the \(x^3\) coefficient must be non-zero. At (a=2), \(a^2-4=0\) and (a+2=4).
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If (p(x)=(k-3)x-2+(2k-6)x+11) has degree (0), what is (k)?
C. (3)
घात (0) के लिए चर वाले दोनों गुणांक शून्य होने चाहिए। (k-3=0) और (2k-6=0) दोनों से (k=3) मिलता है। / For degree (0), both variable-term coefficients must be zero. Both (k-3=0) and (2k-6=0) give (k=3).
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Which expression is not a polynomial in (x) because it contains a term like \(\cos x\)?
B. \(3x^2+\cos x\)
बहुपद के पद चर की निश्चित शून्य या धनात्मक पूर्णांक घातों में होते हैं। \(\cos x\) ऐसा पद नहीं है। / Polynomial terms use fixed non-negative integer powers of the variable. \(\cos x\) is not such a term.
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After simplifying \(\frac{x^4+x^2+x}{x}\) for \(x\neq0\), which polynomial is obtained?
A. \(x^3+x+1\)
हर पद को (x) से भाग देने पर \(x^3+x+1\) मिलता है। इसमें सभी घातें शून्य या धनात्मक पूर्णांक हैं। / Dividing each term by (x) gives \(x^3+x+1\). All its powers are non-negative integers.
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If (q(x)=(a+2)x-6+(a-4)x-5+3) has degree exactly (5), what is the value of (a)?
B. (-2)
घात (5) के लिए \(x^6\) का गुणांक शून्य और \(x^5\) का गुणांक अशून्य होना चाहिए। (a=-2) पर (a-4=-6) अशून्य रहता है। / For degree (5), the \(x^6\) coefficient must be zero and the \(x^5\) coefficient must be non-zero. At (a=-2), (a-4=-6) remains non-zero.
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If (p(x)=(a-1)x-3+(a-1)x-2+(a-1)x+5) is a constant polynomial, what is (a)?
A. (1)
स्थिर बहुपद के लिए सभी चर पदों के गुणांक शून्य होने चाहिए। (a-1=0) से (a=1) मिलता है और (5) बचता है। / For a constant polynomial, all variable-term coefficients must be zero. From (a-1=0), (a=1), and (5) remains.
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Which expression is a polynomial in (x) but not a linear polynomial in (x)?
B. \(x^3+1\)
\(x^3+1\) बहुपद है, पर इसकी घात (3) है। रैखिक बहुपद की घात (1) होती है। / \(x^3+1\) is a polynomial, but its degree is (3). A linear polynomial has degree (1).
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If (p(x)=x-4+cx-3+dx-2+e), under what condition is its degree definitely (4)?
A. किसी भी (c), (d), (e) के लिएFor any (c), (d), (e)
\(x^4\) का गुणांक (1) है, जो कभी शून्य नहीं होता। इसलिए घात हमेशा (4) रहेगी। / The coefficient of \(x^4\) is (1), which is never zero. Therefore, the degree is always (4).
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Which expression is not a polynomial because (x) is hidden in the denominator?
B. \(\frac{x^2+4}{x^2}\)
\(\frac{x^2+4}{x^2}=1+\frac{4}{x^2}\) है। \(\frac{4}{x^2}=4x^{-2}\), इसलिए यह बहुपद नहीं है। / \(\frac{x^2+4}{x^2}=1+\frac{4}{x^2}\). Since \(\frac{4}{x^2}=4x^{-2}\), it is not a polynomial.
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Which expression is a quadratic trinomial polynomial?
A. \(x^2-5x+6\)
\(x^2-5x+6\) की घात (2) है और इसमें तीन पद हैं। इसलिए यह द्विघात त्रिपदी है। / \(x^2-5x+6\) has degree (2) and three terms. Therefore, it is a quadratic trinomial.
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