A symbol having a fixed value is called a $.........$
- ACoefficient.
- BVariable.
- CNone of these.
- ✓Constant.
Answer: D.
View full solution →Question types
Polynomials question types
509 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
509
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
74 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.
If $\text{x}+\frac{1}{\text{x}}=3,$ then $\text{x}^6+\frac{1}{\text{x}^6}=$
- A$927$
- B$414$
- C$364$
- ✓$322$
Answer: D.
View full solution →A polynomial containing one nonzero term is called a $.......$
- ANone of these.
- ✓Monomial.
- CBinomial.
- DTrinomial.
Answer: B.
View full solution →Which of the following polynomials has $(-3)$ as a zero$?$
- A$x^2+3$
- B$x^2-3 x$
- ✓$x^2-9$
- D$(x-3)$
Answer: C.
View full solution →The value of the polynomial $5 x-4 x^2+3$, when $x = -1$ is:
- A$6$
- ✓$-6$
- C$1$
- D$-1$
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 linear polynomial has one and only one zero always.
Reason: Zero of polynomial $x^2-4 x+3$ are $1,3.$
Assertion: A linear polynomial has one and only one zero always.
Reason: Zero of polynomial $x^2-4 x+3$ are $1,3.$
- 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: The constant polynomial $0$ is called zero polynomial.
Reason: $\sqrt{\text{x}}+3$ is a polynomial.
Assertion: The constant polynomial $0$ is called zero polynomial.
Reason: $\sqrt{\text{x}}+3$ is a polynomial.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
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: $p(x)=x^5$ degree $=5$.
Reason: $4\sqrt{\text{t}}+\text{t}^6$ degree is $6.$
Assertion: $p(x)=x^5$ degree $=5$.
Reason: $4\sqrt{\text{t}}+\text{t}^6$ degree is $6.$
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
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: $x^3+x$ has only one real zero.
Reason: A quadratic polynomial can have at most two zero.
Assertion: $x^3+x$ has only one real zero.
Reason: A quadratic polynomial can have at most two zero.
- 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 quadratic polynomial can have at most two zero.
Reason: $x^2+7 x+9$ has two zero.
Assertion: A quadratic polynomial can have at most two zero.
Reason: $x^2+7 x+9$ has two zero.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →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.
A polynomial cannot have more than one zero.
Write whether the following statement are True or False.
Zero of a polynomial is always $0.$
View full solution →Zero of a polynomial is always $0.$
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.
A binomial can have atmost two terms.
A binomial can have atmost two terms.
Factories : $64 a^3-27 b^3-144 a^2 b+108 a b^2$
View full solution →Factorise : $27-125 a^3-135 a+225 a^2$
View full solution →Factorise : $8 a^3-b^3-12 a^2 b+6 a b^2$
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 : $x^3+y^3=(x+y)\left(x^2-x y+y^2\right)$
View full solution →Verify : $x^3-y^3=(x-y)\left(x^2+x y+y^2\right)$
View full solution →Factorise : $27 p^3-\frac{1}{216}-\frac{9}{2} p^2+\frac{1}{4} p$.
View full solution →Factorise : $8 a^3+b^3+12 a^2 b+6 a b^2$
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 $x^3+y^3+z^3-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^2+(y-z)^2+(z-x)^2\right]$.
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 $x^3+3 x^2+3 x+1$ 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 $y\ m$. 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 $y\ m$. 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 $652 m^3$
$1.$ 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 $2,608 m^3.$
$D.$ The length of Container $3$ is $4$ times the length of Container $2.$
$3.$ What is the height of each container$?$
View full solution →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 $652 m^3$
$1.$ 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 $2,608 m^3.$
$D.$ 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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