Sample QuestionsPolynomials questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which is the following is a linear polynomials?
- ✓
$x + 5$
- B
$x^2+5$
- C
$x^3+5$
- D
$x^4+5$
Answer: A.
View full solution →Multiply $\left(x^2-3\right)\left(2 x-7 x^3+4\right)$ and write the degree of the product.
Answer: A.
View full solution →If $x-1$ is a factor of the polynomial $3 x^2+m x$, then find the value of $m$.
Answer: C.
View full solution →When $x=-1$, what is the value of the polynomial $2 x^3+2 x ?$
Answer: A.
View full solution →$p ( x )= x ^2- x +3$, then $p (7 \sqrt{ } 7)=$ ?
- A
$3$
- B
$7 \sqrt{ } 7$
- C
$42 \sqrt{ } 7+3$
- ✓
$49 \sqrt{ } 7$
Answer: D.
View full solution →Write the degree of the polynomial for each of the following: $ax ^7+ bx ^9$ ( $a , b$ are constants)
View full solution →Write the degree of the polynomial for each of the following : $7=7 x ^0$
View full solution →Write the degree of the polynomial for each of the following: $5+3 x^4$
View full solution →Factorize : $6 x^2-5 x-6$
View full solution →Factorize: $63 x^2+5 x-2$
View full solution →Add : $3 m^2 n+5 m n^2-7 m n$ and $2 m^2 n-m n^2+m n$.
View full solution →Multiply : $\left(m^2-5\right) \times\left(m^3+2 m-2\right)$
View full solution →Subtract : $5 a^2-2 a$ from $7 a^2+5 a+6$.
View full solution →Find the factors of the polynomials given below : $\frac{1}{2} x^2-3 x+4$
View full solution →Find the factors of the polynomials given below: $\sqrt{3} x^2+4 x+\sqrt{3}$
View full solution →We have seen the example of expenditure and income (in terms of polynomials) of Govind who is a dry land farmer. He has borrowed rupees one lakh twenty-five thousand from the bank as an agriculture loan and repaid the said loan at 10 p.c.p.a.
He had spent ₹ 10,000 on seeds. The expenses on soyabean crop was ₹ 2000x for fertilizers and pesticides and ₹ $4000 x^2$ was spent on wages and cultivation. He spent $₹ 8000 y$ on fertilizers and pesticides and $₹ 9000 y^2$ on cultivation and wages for cotton and tur crop.
His total income was
$\text { ₹ }\left(14000 x^2+\frac{25000}{3} y^2+16000 y\right)$
By taking $x=2, y=3$ write the income expenditure account of Govind's farming.
View full solution →Read the following passage, write the appropriate amount in the boxes and discuss.
Govind, who is a dry land farmer from Shiralas has a $5$ acre field. His family includes his wife, two children and his old mother. He borrowed one lakh twenty five thousand rupees from the bank for one year as agricultural loan at 10 p.c.p.a. He cultivated soyabean in x acres and cotton and tur in y acres. The expenditure he incurred was as follows :
He spent $₹10,000$ on seeds. The expenses for fertilizers and pesticides for the soyabean crop was$ ₹ 2000x$ and $₹ 4000x^2$ were spent on wages and cultivation of land. He spent ₹ 8000y on fertilizers and pesticides and ₹ 9000y2 for wages and cultivation of land for the cotton and tur crops.Let us write the total expenditure on all the crops by using variables x and y.
$₹ 10000 + 2000x + 4000\times 2 + 8000y + 9000y^2$
He harvested $5 x^2$ quintals soyabean and sold it at $₹ 2800$ per quintal. The cotton crop yield was $\frac{5}{3} y ^2$ quintals which fetched $₹ 5000$ per quintal.
The tur crop yield was $4y$ quintals and was sold at $₹ 4000$ per quintal. Write the total income in rupees that was obtained by selling the entire farm produce, with the help of an expression using variables x and y.
View full solution →Factorise: $(x+2)(x-3)(x-7)(x-2)+64$
View full solution →Factorise : $\left(y^2-3 y\right)^2-5\left(y^2-3 y\right)-50$.
View full solution →If the polynomial $t^3-3 t^2+k t+50$ is divided by $(t-3)$, the remainder is 62 . Find the value of $k$.
View full solution →Divide the polynomial $(2y^4 - 3y^3 + 5y - 4) ÷ (y - 1)$ By synthetic division method and Linear method.
View full solution →Divide the polynomial $(3x^3 + 2x^2 - 1)$ by $(x + 2)$. By synthetic division method and Linear method.
View full solution →Ex (5) Divide $\left(2+2 x^2\right) \div(x+2)$ and write the answer in the given form Dividend $=$ Divisor $\times$ Quotient + Remainder
View full solution →i. If $p(x)=2+5 x$, then find the value of $p(2)+p(-2)-p(1)$.
ii. If $p(x)=2 x^2-5 \sqrt{ } 3 x+5$, then find the value of $p(5 \sqrt{ } 3)$.
View full solution →By using factor theorem in the following examples, determine whether $q(x)$ is a factor of $p(x)$ or not.
i. $p(x)=x^3-x^2-x-1 ; q(x)=x-1$
ii. $p(x)=2 x^3-x^2-45 ; q(x)=x-3$
View full solution →1. Divide $p(x) = 3x^2 + x + 7 by x + 2.$ Find the remainder.
2. Find the value of $p(x) = 3x^2 + x + 7 $ when $x = – 2.$
3. See whether remainder obtained by division is same as the value of $p(-2)$. Take one more example and verify.
View full solution →If $x-2$ and $x-\frac{1}{2}$ both are the factors of the polynomial $n x^2-5 x+m$, then show that $m=$ $n=2$
View full solution →Find the value of the polynomial $2x – 2x^3 + 7$ using given values for $x$.
i. $x = 3$
ii. $x = -1$
iii. $x = 0$
View full solution →Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder :
$(y^3 – 3y^2 + 5y – 1) ÷ (y – 1)$
View full solution →Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder : $(x^4 – 3x^2 – 8) ÷ (x + 4)$
View full solution →