Polynomials

Q.

$(2x^2+3xy+4x{y}^2+5z)\text{is an algebraic expression.}$

1. False
2. True

Q.

Identify the like terms in each of the following algebraic expressions.

$x^2-2y^2+7x^2-9y^2+2xy-xy$

Q.

What is (2x+3x+4y+7y) binomial or polynomial

Q.

Distance between Mumbai and Pune is $(2y^2+y+2)$. There are two routes to travel from Mumbai to Pune as shown in the figure.

What is the difference between the distance covered through the two routes?

1. 57 units
2. 32 units
3. 23 units
4. 34 units

Q. $4x^3-8x^2+8x+1,$ when divided by a polynomial $g\left(x\right)$ gives $2x-1$ as quotient and $x-3$ as remainder. Find $g\left(x\right).$

Q. Distance between Mumbai and Pune is $(2y^2+y+2)$. There are two routes to travel from Mumbai to Pune as shown in the figure.

What is the difference between the distance covered through the two routes?

1. 32 units
2. 23 units
3. 57 units
4. 34 units

Q. 1+2x+4y+8z is a _______________

1. Trinomial
2. Binomial
3. Polynomial
4. Monomial

Q. Let $f\left(x\right)=(x^3+2{)}^{30}$. If $f^n\left(x\right)$ is a polynomial of degree $20$, where $f^n\left(x\right)$ denotes the nth order derivative of $f\left(x\right)$ with respect to x, then the value of n is?

1. $60$
2. $40$
3. $70$
4. $50$

Q. If a sequence or series is not directly in $\text{A.P}$ or $\text{G.P}$, then their general terms $\left(l_n\right)$ cannot be determined easily. For such cases to determine $t_n$ we use the following steps.
Step 1: First of all we find the successive difference (first difference, second difference, third difference $\dots$ so on).
Step 2: If first successive difference is in $\text{A.P}$, then general term can be taken as $t_n=a{n}^2+bn+c$ (i.e. consider $t_n$ as quadratic polynomial in the decreasing power of $n$ with constants $a,b,c$ ).
Step 3: If the second, third successive differences are in $\text{A.P}$, then $t_n=a{n}^3+b{n}^2+cd+d$ for second successive difference in $\text{A.P}$ and so on where $a,b,c,d$ are constants whose order can be changed.
Step 4: If the first difference in step 1 is in $\text{G.P}$, then take $t_n=a{r}^{n-1}+bn+c$. Similarly if second, third difference are in $\text{G .P}$, then general terms are considered by $t_n=a{r}^{n-1}+b{n}^2+cn+d$ and $t_n=a{r}^{n-1}+b{n}^3+c{n}^2+dn+e$ respectively where $a,b,c,d,e\dots$ are constants whose orders can be changed.
Now consider the sequences
$P:9,16,29,54,103,\dots$
$Q:4,14,30,52,80,114,\dots$
$R:2,12,36,80,150,252,\dots$
$S:2,5,12,31,86,\dots$
On the basis of above data (information) answer the following questions:If $n^{th}$ term of sequence $P$ & $R$ are respectively of the forms $a{2}^{n-1}+bn+c$ & $A+Bn+C{n}^2+D{n}^3$, then the value of $(a+b+c)(A+B+C+D)$ equals

1. $0$
2. $18$
3. $9$
4. $12$

Q.

Identify the like terms in each of the following algebraic expression.

$5x^2-3xy+2x^2-1$

Q.

Identify the like terms in each of the following algebraic expressions.

$2x^4{y}^2-3x{y}^2+7y^2{x}^2-2y^{2}x+6$

Q.

Distance between Mumbai and Pune is $(2y^2+y+2)$. There are two routes to travel from Mumbai to Pune as shown in the figure.

What is the difference between the distance covered through the two routes?

1. 32 units

2. 23 units

3. 34 units

4. 57 units

Q.

$2x^2-3x+4$, when $x=-2$.

Q.

Identify the monomial among the following.

1. 3b + c

2. 4b

3. 2a + 6b + 5c

4. a +1

Q. 35xy + 45x + 5y² + 25xyz is a ______.

1. polynomial
2. monomial
3. trinomial
4. binomial

Q.

35xy + 45x + 5y² + 25xyz is a ______.

1. Monomial

2. Trinomial

3. Binomial

4. Polynomial