Addition of Polynomials

Q. Question 8
If a + b + c = 5 and ab + bc + ca = 10, then prove that $a^3+b^3+c^3-3abc=-25$.

Q.

If 3x + 2y = 12 and xy = 6, find the value of 9x2+ 4y2

Q.

Add: $11x^2-8x+4$ and $6x^2+7x-10$.

1. $17x^2-x-6$

2. $17x^2-x+6$

3. $17x^2+x-6$

4. $18x^2-x-6$

Q.

8x³ - 343y³ = ?

1. (2x + 7y) (2x - 7y)

2. (2x-7y) (4x² + 14xy + 49y²)

3. (2x - 7y) (4x² - 49y²)

4. (2x+7y)(4x² - 14xy + 49y²)

Q.

If $(3x-1{)}^7=a_7{x}^7+a_6{x}^6+...............a_1+a_0$, then find the value of $a_7+a_6+..a_0$

Q.

Multiply $(7x-4x^2+2x^3-5)$ with $(3x-2)$.

1. $6x^4-16x^3+29x^2-x+1$

2. $6x^4-16x^3+27x^2-x+10$

3. $5x^4-16x^3+29x^2-x+10$

4. $6x^4-16x^3+29x^2-29x+10$

Q.

Write the constant term:

^{​​​​​} :X³+2x+1/5-7/2 x²-x⁶

Q. Question 7
Find the value of the polynomial $3x^3–4x^2+7x–5$, when x = 3 and also when x = -3.

Q.

The sum of $12abx$, $2a^{2}bx$, $8abx$ and $8a^{2}bx$ is

1. $10abx$ + $20a^{2}bx$

2. $30a^3{b}^2{x}^2$

3. $20abx$ + $10a^{2}bx$

4. none of the above

Q. Question 2
Find p(0), p(1) and p(2) for each of the following polynomials:
(i) $p\left(y\right)=y^2-y+1$
(ii) $p\left(t\right)=2+t+2t^2-t^3$
(iii) $p\left(x\right)=x^3$
(iv) $p\left(x\right)=(x-1)(x+1)$

Q.

Find the sum of the following expressions: $3a-4b+5c,2a+3b-6c,-5a+8b+7c$

Q.

Identify the like terms in the following groups of terms $2xy,yz,3z,\frac{1}{2}yz$

Q.

What is $(x-y{)}^3$?

1. $x^3-y^3+3xy(x-y)$
   
   
2. $x^3-y^3-3xy(x-y)$
   
3. $x^3+y^3+3xy(x+y)$
   
4. $x^3+y^3-3xy(x+y)$
   

Q. must be subtracted from $(x^3-3x^2+5x-1)$ to get $(2x^3+x^2-4x+2)$ .

1. $-x^3-4x^2+9x-3$
2. $-x^3-4x^2+9x-9$
3. $-x^3-4x^2+6x-3$

Q. Match the following polynomials with corresponding value of maximum number of zeroes.

1. 6
2. 99
3. 100
4. 16

Q.

$(2x-3y{)}^3+(x+3y{)}^3+3(2x-3y{)}^2(x+3y)+3(2x-3y\left)\right(x+3y{)}^2=$

1. 
2. 
3. 
4. 

Q.

Add.$2a+8b+10,-3a+7b+16,2b-5$

Q.

You had a certain number of chocolates. (You don't know the number of chocolates) If you receive the same number of chocolates from your friend and another friend gives you thrice the number of chocolates you initially had, which of the following can represent the number of chocolates you have in all now ?

1. $x+4y$ (x and y both are different variables)

2. $x+3xy$ (x and y both are different variables)

3. $5x$

4. $x^4$

Q. Find the number of terms in the given algebraic expression.

$2x^3+4x^2+9x+8$

1. 4
2. 3
3. 2
4. 5

Q.

If 2x – 3y = 1, then express $4x^2-2x+3$ in terms of y.

1. 9y² – 3y + 3

2. 9y² – 2y + 3

3. y² – 3y + 4

4. 9y² + 3y + 3

Q.

When $7xy+5yz-3zx$, $4yz+9zx-4y$ and $-3xz+5x-2xy$ are added, we get $5xy+9yz+3zx+5x-4y$.

1. True

2. False

Q.

If x+y=5 and xy=6, then find x^3+y^3

Q.

Add: $3+2y-5y^2+6y^3,-8+3y+7y^3$ and $5-6y-8y^3+y^2$

1. 

2. 

3. 

4. 

Q. Simplify:

(i) (3x² $-$ 2x + 1) + (x² + 5x $-$ 3) + (4x² + 8)
(ii) (2y³ + 3y $-$ 7) $-$ (8y $-$ 6) + (4y³ $-$ 2y + 1)
(iii) 5m³ $-$ m + 6m² $-$ (3m² $-$ 2 + m)

Q.

What is the product of $(a+b)$ and $7a^2$$b^2$?

1. $7a^2$$b^2$

2. $7a^3{b}^2+7a^2{b}^3$

3. $7a^{2}b+7a{b}^2$

4. $7a^2$$b^3$

Q. (iii) 9x + 11y = 78; 11x + 9y = 82

Q. Addition of the two polynomials $2x^3-3x^2$ and$-5x^3-8x^2$ is .

1. $3x^3-11x^2$
2. $-3x^3+11x^2$
3. $-3x^3-11x^2$

Q. If $x+y=1$ then $x^3+y^3+3xy=............$

1. $0$
2. $1$
3. $2$
4. None of these

Q. Arrange the following in the decreasing order based on the number of terms in the result after addition.

1. x, -x
2. 2x+3y, z+k
3. x+5x, 8y+3y
4. 9x, 6y +z

Q.

Find the third side of a triangle whose two sides are $(3m^2-5m$) and $(4m^2+12$) and perimeter is $(8m^2-9m+4$).

1. $m^2-4m-8$

2. $m^2+4m-8$

3. $m^2-4m+8$

4. $m^2+4m+8$