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778 questions tagged with polynomials.
Which polynomial in (x) has degree (4)?
A. \(x^4+x^2+1\)
The highest power in \(x^4+x^2+1\) is (4). So its degree is (4).
The correct answer is A. \(x^4+x^2+1\). The highest power in \(x^4+x^2+1\) is (4). So its degree is (4).
\(x^4+x^2+1\) में सबसे बड़ी घात (4) है। इसलिए इसकी घात (4) है।
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What is the coefficient of (x) in \(2x^2-9\)?
C. (0)
There is no (x)-term, so its coefficient is (0). In exams, treat the coefficient of a missing term as (0).
The correct answer is C. (0). There is no (x)-term, so its coefficient is (0). In exams, treat the coefficient of a missing term as (0).
इसमें (x) वाला पद लिखा नहीं है इसलिए उसका गुणांक (0) है। परीक्षा में लुप्त पद का गुणांक (0) मानें।
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If (p(x)=ax+b) and \(a\neq0\), what is the degree of (p(x))?
B. (1)
Since \(a\neq0\), the (x)-term is present. Therefore the degree of the polynomial is (1).
The correct answer is B. (1). Since \(a\neq0\), the (x)-term is present. Therefore the degree of the polynomial is (1).
\(a\neq0\) होने से (x) वाला पद मौजूद है। इसलिए बहुपद की घात (1) है।
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For (p(x)=x-2+2x+3), what is the value of (p(-1))?
B. (2)
(p(-1)=(-1)2+2(-1)+3=2). In exams, use brackets while substituting a negative value.
The correct answer is B. (2). (p(-1)=(-1)2+2(-1)+3=2). In exams, use brackets while substituting a negative value.
(p(-1)=(-1)2+2(-1)+3=2)। परीक्षा में ऋणात्मक मान रखते समय कोष्ठक लगाएं।
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What is the leading term of (p(x)=2x-3-7x-2+4x-1)?
A. \(2x^3\)
The term with the highest power is \(2x^3\). This is called the leading term.
The correct answer is A. \(2x^3\). The term with the highest power is \(2x^3\). This is called the leading term.
सबसे बड़ी घात वाला पद \(2x^3\) है। यही अग्र पद कहलाता है।
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What is the coefficient of the missing \(x^4\) term in \(x^5-4x^2+10\)?
C. (0)
A missing term is treated as having coefficient (0). So the coefficient of \(x^4\) is (0).
The correct answer is C. (0). A missing term is treated as having coefficient (0). So the coefficient of \(x^4\) is (0).
जो पद लिखा नहीं है उसका गुणांक (0) माना जाता है। इसलिए \(x^4\) का गुणांक (0) है।
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How is \(4x^2+3x^4-x+2\) written in standard form?
A. \(3x^4+4x^2-x+2\)
In standard form, terms are written in decreasing powers. Therefore \(3x^4+4x^2-x+2\) is correct.
The correct answer is A. \(3x^4+4x^2-x+2\). In standard form, terms are written in decreasing powers. Therefore \(3x^4+4x^2-x+2\) is correct.
मानक रूप में पद घटती घातों में लिखे जाते हैं। इसलिए \(3x^4+4x^2-x+2\) सही है।
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What is the coefficient of \(x^3\) in \(9x^4-2x^3+7\)?
B. \(-2\)
The number attached to \(x^3\) is (-2). So the coefficient of \(x^3\) is (-2).
The correct answer is B. \(-2\). The number attached to \(x^3\) is (-2). So the coefficient of \(x^3\) is (-2).
\(x^3\) के साथ (-2) लगा है। इसलिए \(x^3\) का गुणांक (-2) है।
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What is the degree of \(3x^3+0x^2-2x+5\)?
C. (3)
The highest non-zero power term is \(3x^3\). So the degree is (3).
The correct answer is C. (3). The highest non-zero power term is \(3x^3\). So the degree is (3).
सबसे बड़ी शून्य से भिन्न घात वाला पद \(3x^3\) है। इसलिए घात (3) है।
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Which polynomial is a trinomial?
A. \(x^2+x+1\)
A trinomial has three terms. The expression \(x^2+x+1\) has three terms.
The correct answer is A. \(x^2+x+1\). A trinomial has three terms. The expression \(x^2+x+1\) has three terms.
त्रिपदी में तीन पद होते हैं। \(x^2+x+1\) में तीन पद हैं।
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Which polynomial is a binomial?
B. (5x-7)
A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).
The correct answer is B. (5x-7). A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).
द्विपदी में दो पद होते हैं। (5x-7) में (5x) और (-7) दो पद हैं।
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Which polynomial is a monomial?
A. \(3x^2\)
A monomial has only one term. The expression \(3x^2\) has one term.
The correct answer is A. \(3x^2\). A monomial has only one term. The expression \(3x^2\) has one term.
एकपदी में केवल एक पद होता है। \(3x^2\) एक ही पद है।
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What is the leading coefficient of \(6x^5+x^2-4\)?
A. (6)
The term with the highest power is \(6x^5\). So the leading coefficient is (6).
The correct answer is A. (6). The term with the highest power is \(6x^5\). So the leading coefficient is (6).
सबसे बड़ी घात वाला पद \(6x^5\) है। इसलिए अग्र गुणांक (6) है।
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How many terms are there in (q(x)=x-3+2x-2-x+4)?
C. (4)
It has four terms \(x^3\), \(2x^2\), (-x), and (4). In exams, identify terms separated by (+) or (-).
The correct answer is C. (4). It has four terms \(x^3\), \(2x^2\), (-x), and (4). In exams, identify terms separated by (+) or (-).
इसमें \(x^3\), \(2x^2\), (-x) और (4) चार पद हैं। परीक्षा में पदों को (+) या (-) से अलग पहचानें।
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For the polynomial (p(x)=2x-2-3x+1), what is the value of (p(1))?
A. (0)
(p(1)=2(1)2-3(1)+1=0). In exams, substitute the given value for (x) carefully.
The correct answer is A. (0). (p(1)=2(1)2-3(1)+1=0). In exams, substitute the given value for (x) carefully.
(p(1)=2(1)2-3(1)+1=0)। परीक्षा में (x) की जगह दिए गए मान को सावधानी से रखें।
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What is the coefficient of \(x^2\) in \(5x^4-3x^2+x-6\)?
B. \(-3\)
The number attached to \(x^2\) is (-3). In exams, include the sign of the term in the coefficient.
The correct answer is B. \(-3\). The number attached to \(x^2\) is (-3). In exams, include the sign of the term in the coefficient.
\(x^2\) के साथ लगा संख्या गुणांक (-3) है। परीक्षा में पद का चिह्न भी गुणांक में शामिल करें।
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What is the constant term in the polynomial \(7x^2+5x-11\)?
C. \(-11\)
The constant term is the term without (x). Here the constant term is (-11).
The correct answer is C. \(-11\). The constant term is the term without (x). Here the constant term is (-11).
स्थिर पद वह होता है जिसमें (x) नहीं होता। यहाँ स्थिर पद (-11) है।
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What is the degree of the polynomial (p(x)=4x-3-2x+9)?
A. (3)
The highest power is (3), so the degree of the polynomial is (3). In exams, look at the highest power of the variable.
The correct answer is A. (3). The highest power is (3), so the degree of the polynomial is (3). In exams, look at the highest power of the variable.
सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) है। परीक्षा में सबसे बड़ी चर घात देखें।
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Which expression is a polynomial in one variable (x)?
A. \(3x^2-5x+7\)
The expression \(3x^2-5x+7\) has only (x) and non-negative integer powers. In exams, the variable power must not be negative or fractional.
The correct answer is A. \(3x^2-5x+7\). The expression \(3x^2-5x+7\) has only (x) and non-negative integer powers. In exams, the variable power must not be negative or fractional.
\(3x^2-5x+7\) में केवल (x) है और घातें पूर्ण संख्याएँ हैं। परीक्षा में चर की घात ऋणात्मक या भिन्न नहीं होनी चाहिए।
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What is the simplified form of \(\frac{6b^{-3}+9b^{-3}}{3b^{-5}}\), where \(b\neq0\)?
A. \(5b^{2}\)
The numerator is \(6b^{-3}+9b^{-3}=15b^{-3}\). Thus \(\frac{15b^{-3}}{3b^{-5}}=5b^{2}\).
The correct answer is A. \(5b^{2}\). The numerator is \(6b^{-3}+9b^{-3}=15b^{-3}\). Thus \(\frac{15b^{-3}}{3b^{-5}}=5b^{2}\).
ऊपर \(6b^{-3}+9b^{-3}=15b^{-3}\) है। \(\frac{15b^{-3}}{3b^{-5}}=5b^{2}\) मिलता है।
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What is the simplified form of (\left\(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}\right\)^{-1})?
A. \(9r^{6}s^{-8}\)
Inside, \(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}\). Raising to (-1) gives \(9r^{6}s^{-8}\).
The correct answer is A. \(9r^{6}s^{-8}\). Inside, \(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}\). Raising to (-1) gives \(9r^{6}s^{-8}\).
अंदर \(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}\) है। (-1) घात लेने पर \(9r^{6}s^{-8}\) मिलता है।
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Which option is the simplified form of \(\frac{x^{12}-4096}{x^{6}-64}\), where \(x^{6}\neq64\)?
B. \(x^{6}+64\)
Since (x^{12}-4096=\(x^{6}\)^{2}-64^{2}=\(x^{6}-64\)\(x^{6}+64\)), cancelling the common factor gives \(x^{6}+64\).
The correct answer is B. \(x^{6}+64\). Since (x^{12}-4096=\(x^{6}\)^{2}-64^{2}=\(x^{6}-64\)\(x^{6}+64\)), cancelling the common factor gives \(x^{6}+64\).
(x^{12}-4096=\(x^{6}\)^{2}-64^{2}=\(x^{6}-64\)\(x^{6}+64\))। समान गुणनखंड कटने पर \(x^{6}+64\) मिलता है।
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If (\left\(x^{4}y^{-3}\right\)^{k}=x^{16}y^{-12}), what is the value of (k)?
C. (4)
The left side has exponents (4k) and (-3k). Both (4k=16) and (-3k=-12) give (k=4).
The correct answer is C. (4). The left side has exponents (4k) and (-3k). Both (4k=16) and (-3k=-12) give (k=4).
बाएँ पक्ष में घातें (4k) और (-3k) हैं। (4k=16) और (-3k=-12) दोनों से (k=4) मिलता है।
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What is the simplified form of (\frac{\(5x^{-2}\)^{2}\(2x^{4}\)^{2}}{20x^{4}})?
A. (5)
The numerator is \(25x^{-4}\cdot4x^{8}=100x^{4}\). Thus \(\frac{100x^{4}}{20x^{4}}=5\).
The correct answer is A. (5). The numerator is \(25x^{-4}\cdot4x^{8}=100x^{4}\). Thus \(\frac{100x^{4}}{20x^{4}}=5\).
अंश \(25x^{-4}\cdot4x^{8}=100x^{4}\) है। \(\frac{100x^{4}}{20x^{4}}=5\) मिलता है।
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If \(x^{5}=3\), what is the value of \(x^{15}+x^{10}\)?
B. (36)
Here (x^{15}=\(x^{5}\)^{3}=27) and (x^{10}=\(x^{5}\)^{2}=9). Therefore, the sum is (36).
The correct answer is B. (36). Here (x^{15}=\(x^{5}\)^{3}=27) and (x^{10}=\(x^{5}\)^{2}=9). Therefore, the sum is (36).
(x^{15}=\(x^{5}\)^{3}=27) और (x^{10}=\(x^{5}\)^{2}=9)। इसलिए योग (36) है।
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What is the simplified form of \(\frac{x^{10}-1024}{x^{5}-32}\), where \(x^{5}\neq32\)?
B. \(x^{5}+32\)
We use (x^{10}-1024=\(x^{5}\)^{2}-32^{2}=\(x^{5}-32\)\(x^{5}+32\)). Cancelling the common factor leaves \(x^{5}+32\).
The correct answer is B. \(x^{5}+32\). We use (x^{10}-1024=\(x^{5}\)^{2}-32^{2}=\(x^{5}-32\)\(x^{5}+32\)). Cancelling the common factor leaves \(x^{5}+32\).
(x^{10}-1024=\(x^{5}\)^{2}-32^{2}=\(x^{5}-32\)\(x^{5}+32\))। समान गुणनखंड कटने पर \(x^{5}+32\) बचता है।
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A. (1)
Inside, \(\frac{8x^{-3}y^{2}}{2x^{5}y^{-4}}=4x^{-8}y^{6}\), and its square is \(16x^{-16}y^{12}\). Multiplying by \(\frac{x^{16}}{16y^{12}}\) gives (1).
The correct answer is A. (1). Inside, \(\frac{8x^{-3}y^{2}}{2x^{5}y^{-4}}=4x^{-8}y^{6}\), and its square is \(16x^{-16}y^{12}\). Multiplying by \(\frac{x^{16}}{16y^{12}}\) gives (1).
अंदर \(\frac{8x^{-3}y^{2}}{2x^{5}y^{-4}}=4x^{-8}y^{6}\), इसका वर्ग \(16x^{-16}y^{12}\) है। फिर \(\frac{x^{16}}{16y^{12}}\) से गुणा करने पर (1) मिलता है।
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A. \(\frac{x}{4}\)
Here \(\frac{4x^{-2}}{x^{3}}=4x^{-5}\), so its reciprocal is \(\frac{x^{5}}{4}\), and multiplying by \(x^{-4}\) gives \(\frac{x}{4}\). In exams, simplify the bracket first.
The correct answer is A. \(\frac{x}{4}\). Here \(\frac{4x^{-2}}{x^{3}}=4x^{-5}\), so its reciprocal is \(\frac{x^{5}}{4}\), and multiplying by \(x^{-4}\) gives \(\frac{x}{4}\). In exams, simplify the bracket first.
\(\frac{4x^{-2}}{x^{3}}=4x^{-5}\), इसलिए व्युत्क्रम \(\frac{x^{5}}{4}\) है और \(x^{-4}\) से गुणा करने पर \(\frac{x}{4}\) मिलता है। परीक्षा में पहले कोष्ठक को सरल करें।
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If \(x=\sqrt{2}+\sqrt{5}\), what is the value of \(x^{3}-7x\)?
A. \(10\sqrt{2}+4\sqrt{5}\)
Here \(x^{2}=7+2\sqrt{10}\), so \(x^{3}=17\sqrt{2}+11\sqrt{5}\) and \(x^{3}-7x=10\sqrt{2}+4\sqrt{5}\). In exams, first find \(x^{2}\) and then multiply by (x).
The correct answer is A. \(10\sqrt{2}+4\sqrt{5}\). Here \(x^{2}=7+2\sqrt{10}\), so \(x^{3}=17\sqrt{2}+11\sqrt{5}\) and \(x^{3}-7x=10\sqrt{2}+4\sqrt{5}\). In exams, first find \(x^{2}\) and then multiply by (x).
\(x^{2}=7+2\sqrt{10}\), इसलिए \(x^{3}=17\sqrt{2}+11\sqrt{5}\) और \(x^{3}-7x=10\sqrt{2}+4\sqrt{5}\)। परीक्षा में पहले \(x^{2}\) निकालकर फिर (x) से गुणा करें।
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What is the simplified form of \(\frac{4b^{-2}+6b^{-2}}{5b^{-3}}\), where \(b\neq0\)?
A. (2b)
The numerator is \(4b^{-2}+6b^{-2}=10b^{-2}\). Thus \(\frac{10b^{-2}}{5b^{-3}}=2b\).
The correct answer is A. (2b). The numerator is \(4b^{-2}+6b^{-2}=10b^{-2}\). Thus \(\frac{10b^{-2}}{5b^{-3}}=2b\).
ऊपर \(4b^{-2}+6b^{-2}=10b^{-2}\) है। \(\frac{10b^{-2}}{5b^{-3}}=2b\) मिलता है।
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