Addition and Subtraction of Polynomials

Q. What should be added to $1-x+x^2–2x^3$ to get $x^3$?

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

Q.

The surface area and volume of a rectangular block in which the length is 1 centimetre more than the width and the height is 1 centimetre more than the length.

Q.

If $4mn+16m^{2}n$ balloons are to be distributed among $4mn$ children, how many balloons does each child get, if $m=2$?

1. 7

2. 8

3. 9

4. 10

Q.

Subtract$(8-6x+x^2-7x^3+x^5)$ from$(x^4-6x^3+x^2-3x+1)$.

1. $-x^5+x^4+x^3+3x$

2. $-x^5+x^4+x^3-7$

3. $-x^5+x^4+x^3+3x-7$

4. $-x^5+x^4+4x^3+3x-7$

Q.

What must be subtracted from $(4x^3-3x+5)$ to get $(2x^2-3x^3+5x-2)$ ?

1. $x^3-2x^2-8x+7$

2. $7x^3-2x^2-8x+7$

3. $7x^3+2x^2-8x+7$

4. $7x^3-2x^2-8x+3$

Q. x = a+y and a is constant while y $\alpha$ z, x = 30 when z = 6 and x = 24 when z = 2. Find x when z = 10.

Q. The value of the polynomial p(x) = 3x + 2x + 7 is 32. Find the value of x.

1. 3
2. 5
3. 4
4. 7

Q.

Find the value of following polynomial where a = -2 and p(a) = a³ + a² - 10.

Q. Explain polynomial and factorisation.

Q.

The length of the side of a square-shaped farm whose perimeter is 120ab km is

1. 40ab km

2. 30ab km

3. 20ab km

4. 50ab km

Q. If x²y² + k² = 2kxy, where k is constant, then prove that y varies inversely as x.

Q. If 5y − 3x + 15 = 0, then express y in terms of x.