A polynomial containing two non$-$zero terms is called a $..........$
View full solution →Question types
Polynomials question types
507 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
507
Questions
8
Question groups
5
Question types
01
M.C.Q
309 Q→02Assertion (A) & Reason (B) MCQ
65 Q→03True False[1 Marks ]
6 Q→041 Marks Question
72 Q→052 Marks Questions
41 Q→063 Marks Question
9 Q→075 Marks Questions
3 Q→08Case study (4 Marks)
2 Q→Sample Questions
Polynomials questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following expression is a polynomial.
The factors of $x^2 + 4y^2 + 4y - 4xy - 2x - 8,$ are:
View full solution →If $\text{x}+\frac{1}{\text{x}}=2,$ then $\text{x}^3+\frac{1}{\text{x}^3}=$
View full solution →$(207 \times 193) =$ ?
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $(100 + 4)^3= 1124864.$
Reason: $(x + y)^3= x^3+ y^3+ 3x^2y + 3xy^2$
View full solution →Assertion: $(100 + 4)^3= 1124864.$
Reason: $(x + y)^3= x^3+ y^3+ 3x^2y + 3xy^2$
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- Assertion is true but the reason is false.
- Both assertion and reason are false.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Polynomial is the algebraic equation in the form of single variable.
Reason: Polynomial which has three term are called trinomial.
Assertion: Polynomial is the algebraic equation in the form of single variable.
Reason: Polynomial which has three term are called trinomial.
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- Assertion is true but the reason is false.
- Both assertion and reason are false.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it has no linear term and the constant term is positive.
Reason: The zeroes of the quadratic polynomial x2 + 99x + 127 are both positive.
Assertion: If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it has no linear term and the constant term is positive.
Reason: The zeroes of the quadratic polynomial x2 + 99x + 127 are both positive.
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- Assertion is true but the reason is false.
- Both assertion and reason are false.
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the product of the zeroes of the quadratic polynomial $x^2+ 3x + 5k$ is $-10$ then value of $k$ is$ -2.$
Reason: Sum of zeroes of a quadratic polynomial $ax^2 + bx + c$ is $-\frac{\text{b}}{\text{a}}$
Assertion: If the product of the zeroes of the quadratic polynomial $x^2+ 3x + 5k$ is $-10$ then value of $k$ is$ -2.$
Reason: Sum of zeroes of a quadratic polynomial $ax^2 + bx + c$ is $-\frac{\text{b}}{\text{a}}$
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: B.
View full solution →Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A polynomial can have more than one zero.
Reason: Every real number is zero of zero polynomial.
Assertion: A polynomial can have more than one zero.
Reason: Every real number is zero of zero polynomial.
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- Assertion is true but the reason is false.
- Both assertion and reason are false.
Write whether the following statement are True or False. Every polynomial is a binomial.
Write whether the following statement are True or False. A polynomial cannot have more than one zero.
Write whether the following statement are True or False.
A binomial may have degree 5.
A binomial may have degree 5.
Write whether the following statement are True or False. The degree of the sum of two polynomials degree $5$ is always $5$.
View full solution →Write whether the following statement are True or False.
Zero of a polynomial is always 0.
Zero of a polynomial is always 0.
Factories : $64a^3 - 27b^3 - 144a^2b + 108ab^2$
View full solution →Factorise :$27 - 125a^3 - 135a + 225a^2$
View full solution →Factorise : $8a^3 - b^3 - 12a^2b + 6ab^2$
View full solution →Evaluate using suitable identity: ${\left( {99} \right)^3}$
View full solution →Write ${\left( {\frac{3}{2}x + 1} \right)^3}$ in expanded form.
View full solution →Verify : $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$
View full solution →Verify : $x^3- y^3 = (x - y)(x^2 + xy + y^2)$
View full solution →Factorise : $27p^3 - \frac{1}{216} - \frac{9}{2} p^2 + \frac{1}{4}p.$
View full solution →Factorise : $8a^3 + b^3+ 12a^2b + 6ab^2$
View full solution →Evaluate the using suitable identity: $(998)^3$
View full solution →Write the cube in expanded form: ${\left( {2x + 1} \right)^3}$
View full solution →Verify that $x^3 + y^3 + z^3 - 3xyz = \frac{1}{2}(x + y + z)[(x - y)^2 + (y- z)^2 + (z - x)^2].$
View full solution →Use suitable identity to find the product:
$\left( {x + 4} \right)\left( {x + 10} \right)$
View full solution →$\left( {x + 4} \right)\left( {x + 10} \right)$
Find the remainder when $x^3 + 3x^2 + 3x + 1$ is divided by $x$.
View full solution →Verify $x = - \frac{1}{{\sqrt 3 }},\frac{2}{{\sqrt 3 }}$ are zeroes of the polynomial $p\left( x \right) = 3{x^2} - 1$
View full solution →Find the remainder obtained on dividing $p(x) = x^3 + 1$ by $x + 1.$
View full solution →Divide the polynomial $3x^4 – 4x^3 – 3x –1$ by $x – 1$
View full solution →Divide $p(x)$ by $g(x),$ where $p(x) = x + 3x^2 – 1$ and $g(x) = 1 + x$
View full solution →Hard plastic square shaped sheets are available in the.
The side length of sheets is as per requirement.
The price of a sheet is z per square meter.
Anuj requires two sheets – a smaller sheet with side length x m and a larger sheet with side length ym. He has two choices:
Choice 1 – buy two separate sheets of side lengths x m and y m
Choice 2 – buy a single sheet with side length (x+ y) m
4. What is the height of each container?
5. What is the difference in price between the two choices?
6. The area of a rectangle is $\left(3 x^2+x-2\right)$ square units. Its width is $(1+x)$ units. What is the length of the rectangle?
7. A polynomial is expressed as $x^3+b x^2+c x+d=0$. The same polynomial can be written in factor form as $x+p x+q x+r=0$.
How is the constant term in the polynomial related to its factors p, q, and r?
A. $d=p+q+r$
B. $d=(p+q) \times r$
C. $d=p \times q \times r$
D. $d=p q+q r+p r$
8. A polynomial is divided by $(x-1)$. The quotient obtained is $3 x^3-x^2-x-4$, and the remainder is -5 . Which polynomial meets these conditions?
A. $3 x^3-x^2-x-9$
B. $3 x^3-x^2-x-4$
C. $3 x^4-4 x^3-3 x+4$
D. $3 x^4-4 x^2-3 x-1$
9. What is the common factor of $x^3-x^2$ and $-22 x^2+142 x-120 ?$
A. x
B. (x – 1)
C. $x^2$
D. 1
10. A polynomial is expressed as: $p (x)=x^3+x^2-x-1$
At what values of $x$ is the polynomial $p (x)=0$ ?
View full solution →The side length of sheets is as per requirement.
The price of a sheet is z per square meter.
Anuj requires two sheets – a smaller sheet with side length x m and a larger sheet with side length ym. He has two choices:
Choice 1 – buy two separate sheets of side lengths x m and y m
Choice 2 – buy a single sheet with side length (x+ y) m
4. What is the height of each container?
5. What is the difference in price between the two choices?
6. The area of a rectangle is $\left(3 x^2+x-2\right)$ square units. Its width is $(1+x)$ units. What is the length of the rectangle?
7. A polynomial is expressed as $x^3+b x^2+c x+d=0$. The same polynomial can be written in factor form as $x+p x+q x+r=0$.
How is the constant term in the polynomial related to its factors p, q, and r?
A. $d=p+q+r$
B. $d=(p+q) \times r$
C. $d=p \times q \times r$
D. $d=p q+q r+p r$
8. A polynomial is divided by $(x-1)$. The quotient obtained is $3 x^3-x^2-x-4$, and the remainder is -5 . Which polynomial meets these conditions?
A. $3 x^3-x^2-x-9$
B. $3 x^3-x^2-x-4$
C. $3 x^4-4 x^3-3 x+4$
D. $3 x^4-4 x^2-3 x-1$
9. What is the common factor of $x^3-x^2$ and $-22 x^2+142 x-120 ?$
A. x
B. (x – 1)
C. $x^2$
D. 1
10. A polynomial is expressed as: $p (x)=x^3+x^2-x-1$
At what values of $x$ is the polynomial $p (x)=0$ ?
A shipment service provider uses three types of containers for shipping materials. The height and
width of the three containers are the same. The containers’ height is 0.15 m more than their width, and the volume of the smallest container is 652 m³
width of the three containers are the same. The containers’ height is 0.15 m more than their width, and the volume of the smallest container is 652 m³
1. Write a polynomial relating Container 1’s length, breadth and height with its volume.
2. Which of the following statements is true?
A. The volume of the three containers is the same.
B. The length of the three containers is the same.
C. The volume of Container 3 is 2,608 m³.
D. The length of Container 3 is 4 times the length of Container 2.
3. What is the height of each container?
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