When p(x) = 4x3 - 12x2 + 11x - 5 is divided by (2x - 1), the remainder is:
- A0
- B-5
- C-2
- D2
Question types
Polynomials question types
413 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
413
Questions
8
Question groups
5
Question types
01
M.C.Q
273 Q→02True False[1 Marks ]
6 Q→031 Marks Question
74 Q→04Match the Following.
7 Q→052 Marks Questions
39 Q→063 Marks Question
7 Q→074 Marks Questions
5 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.
$\sqrt{2}$ is a polynomial of degree.
- A0
- B1
- C2
- D$\sqrt{2}$
The zeros of the polynomial p(x) = 2x2 + 5x - 3 are.
- A$1,\frac{-1}{2}$
- B$\frac{-1}{2},3$
- C$\frac{1}{2},-3$
- D$\frac{1}{2},3$
When p(x) = x4 + 2x3 - 3x2 + x - 1 is divided by (x - 2), the remainder is:
- A21
- B0
- C-1
- D-15
The value of $\frac{(2.3)^3-0.027}{(2.3)^2+0.69+0.09},$ is:
- A2
- B3
- C2.327
- D2.273
Every polynomial is a binomial.
A polynomial cannot have more than one zero.
A binomial may have degree 5.
The degree of the sum of two polynomials degree 5 is always 5.
Zero of a polynomial is always 0.
Factories : 64a3 - 27b3 - 144a2b + 108ab2
Factorise :27 - 125a3 - 135a + 225a2
Factorise : 8a3 - b3 - 12a2b + 6ab2
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 →| 'A' | 'B' | ||
| Q.1. | Factors of $x^2-x-12$ | A. | (x-10) (x + 10) |
| Q.2. | Factors of $x^2-100$ | B. | (x-20) (x - 5) |
| C. | (x-4) (x + 3) |
| 'A' | 'B' | ||
| Q.1. | 105 × 95 =__________ | A. | 6400 |
| Q.2. | 77 x 83 =__________ | B. | 9975 |
| C. | 6391 |
| 'A' | 'B' |
| Q.1. $(x+3)(x-2)=\ldots \ldots$ | (a) $x^2+x-6$ |
| Q.2. $(x-3)(x+2)=\ldots\ldots$ | (b) $x^2-x-6$ |
| (c) $x^2-5 x+6$ |
| 'A' | 'B' |
| Q.1. $(x+2)(x-2)=\ldots \ldots$ | (a) $x^2-4 x+4$ |
| Q.2. $(x+2)(x+2)=\ldots \ldots$ | (b) $x^2+4 x+4$ |
| (c) $x^2-4$ |
| 'A' | 'B' |
| Q.1. $x^2-49=\ldots\ldots$ | (a) $(x+7)(x+7)$ |
| Q.2. $x^2-14 x+49=\ldots\ldots$ | (b) $(x-7)(x-7)$ |
| (c) $(x - 7)(x+7)$ |
Verify : x3 + y3 = (x + y)(x2 - xy + y2)
Verify : x3 - y3 = (x - y)(x2 + xy + y2)
Factorise : 27p3 - $\frac{1}{216}$ - $\frac{9}{2}$p2 + $\frac{1}{4}$p.
View full solution →Factorise : 8a3 + b3 + 12a2b + 6ab2
Evaluate the using suitable identity: (998)3
Write the cube in expanded form: ${\left( {2x + 1} \right)^3}$
View full solution →Verify that x3 + y3 + z3 - 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 x3 + 3x2 + 3x + 1 is divided by x.
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 →Complete the following example using Nityasam.
$\begin{array}{c}(i)(2 a-7 b)^3=(2 a)^3+(-7 b)^3+3(2 a)(-7 b)(\_\_\_\_\_\_) \\ =\_\_\_\_\_\_+\left(-343 b^3\right)+(-42 a b)(2 a-7 b) \\ =8 a^3-\_\_\_\_\_\_\_-84 a^2 b+\_\_\_\_\_\_\end{array}$
$\begin{array}{c}(ii) 95 \times 105=(100+\_\_\_\_\_\_)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-(\_\_\_\_\_\_)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\\=9975\end{array}$
View full solution →$\begin{array}{c}(i)(2 a-7 b)^3=(2 a)^3+(-7 b)^3+3(2 a)(-7 b)(\_\_\_\_\_\_) \\ =\_\_\_\_\_\_+\left(-343 b^3\right)+(-42 a b)(2 a-7 b) \\ =8 a^3-\_\_\_\_\_\_\_-84 a^2 b+\_\_\_\_\_\_\end{array}$
$\begin{array}{c}(ii) 95 \times 105=(100+\_\_\_\_\_\_)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-(\_\_\_\_\_\_)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\\=9975\end{array}$
Complete the following example using Nityasam.
$\begin{array}{c}(i)(4 x+3 y)^3=(4 x)^3+(3 y)^3+3(4 x)(3 y)\left(\_\_\_\_\_\_\right) \\ =\_\_\_\_\_\_+27 y^3+36 x y(4 x+3 y) \\ =64 x^3+\_\_\_\_\_\_+144 x^2 y+\_\_\_\_\_\_\end{array}$
$\begin{array}{c}(ii) 106 \times 94=(100+\_\_\_\_\_\_)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-(\_\_\_\_\_\_)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\\=9964\end{array}$
View full solution →$\begin{array}{c}(i)(4 x+3 y)^3=(4 x)^3+(3 y)^3+3(4 x)(3 y)\left(\_\_\_\_\_\_\right) \\ =\_\_\_\_\_\_+27 y^3+36 x y(4 x+3 y) \\ =64 x^3+\_\_\_\_\_\_+144 x^2 y+\_\_\_\_\_\_\end{array}$
$\begin{array}{c}(ii) 106 \times 94=(100+\_\_\_\_\_\_)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-(\_\_\_\_\_\_)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\\=9964\end{array}$
Complete the following example using Nityasam.
$\begin{array}{c}(i)(5 x+2 y)^3=(5 x)^3+(2 y)^3+3(5 x)(2 y)(\_\_\_\_\_\_) \\ =\_\_\_\_\_\_+8 y^3+30 x y(5 x+2 y) \\ =125 x^3+\_\_\_\_\_\_+150 x^2 y+\_\_\_\_\_\_\end{array}$
$\begin{array}{c}(ii) 108 \times 92=(100+\_\_\_\_\_\_)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-(\_\_\_\_\_\_)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\\=9936\end{array}$
View full solution →$\begin{array}{c}(i)(5 x+2 y)^3=(5 x)^3+(2 y)^3+3(5 x)(2 y)(\_\_\_\_\_\_) \\ =\_\_\_\_\_\_+8 y^3+30 x y(5 x+2 y) \\ =125 x^3+\_\_\_\_\_\_+150 x^2 y+\_\_\_\_\_\_\end{array}$
$\begin{array}{c}(ii) 108 \times 92=(100+\_\_\_\_\_\_)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-(\_\_\_\_\_\_)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\\=9936\end{array}$
Complete the following example using Nityasam.
$\begin{array}{c}(i)(2 x+5 y)^3=(2 x)^3+(5 y)^3+3(2 x)(5 y)\left(\_\_\_\_\_\_\right) \\ =\_\_\_\_\_\_+125 y^3+30 x y(2 x+5 y) \\ =8 x^3+\_\_\_\_\_\_+60 x^2 y+\_\_\_\_\_\_\end{array}$
$\begin{array}{l}(ii) 112 \times 88=\left(100+\_\_\_\_\_\_\right)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-\left(\_\_\_\_\_\_\right)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\ \\ =9856\end{array}$
View full solution →$\begin{array}{c}(i)(2 x+5 y)^3=(2 x)^3+(5 y)^3+3(2 x)(5 y)\left(\_\_\_\_\_\_\right) \\ =\_\_\_\_\_\_+125 y^3+30 x y(2 x+5 y) \\ =8 x^3+\_\_\_\_\_\_+60 x^2 y+\_\_\_\_\_\_\end{array}$
$\begin{array}{l}(ii) 112 \times 88=\left(100+\_\_\_\_\_\_\right)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-\left(\_\_\_\_\_\_\right)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\ \\ =9856\end{array}$
Complete the following example using Nityasam.
$\begin{aligned}(i)(3 a+4 b)^3 & =(3 a)^3+\left(\_\_\_\_\_\_\right) +3(3 a)(4 b)\\ & =27 a^3+\left(\_\_\_\_\_\_\right)+36 a b(3 a+4 b) \\ & =27 a^3+64 b^3+\left(\_\_\_\_\_\_\right)+144 a b^2 \end{aligned}$
$\begin{array}{c}(ii) 104 \times 96=\left(100+\_\_\_\_\_\_\right)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-\left(\_\_\_\_\_\_\right)^2 \\ =\left(\_\_\_\_\_\_\right)-16 \\ =9984\end{array}$
View full solution →$\begin{aligned}(i)(3 a+4 b)^3 & =(3 a)^3+\left(\_\_\_\_\_\_\right) +3(3 a)(4 b)\\ & =27 a^3+\left(\_\_\_\_\_\_\right)+36 a b(3 a+4 b) \\ & =27 a^3+64 b^3+\left(\_\_\_\_\_\_\right)+144 a b^2 \end{aligned}$
$\begin{array}{c}(ii) 104 \times 96=\left(100+\_\_\_\_\_\_\right)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-\left(\_\_\_\_\_\_\right)^2 \\ =\left(\_\_\_\_\_\_\right)-16 \\ =9984\end{array}$
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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