Polynomials

Q.

if a+b+c=6 , a²+b²+c²=14 and a³+b³+c³=36 then find the value of (abc) ?

Q. Prove that :(a-b)^3+(b-c)^3+(c-a)^3 = 3(a-b) (b-c) (c-a)

Q. (81/256​​​)^{-3/4
How to solve☝☝}

Q. If (ax^3 + 2)^2 = a^2*x^6 + x^3 + 4, then find a.

Q. Evaluate the following: (-67)^3+(35)^3+(32)^3

Q.

If 9^x*3^2*[-x/3²]^-2​​​​​​=1/27, find x

Q.

Is 2x^{​​​​​​2} - 2_/x a polynomial?

Q. The series : 1, 3, 5, 7, ... can be represented by a general term which is .

1. 2n-1
2. 2n+3
3. 3n
4. 3n+3

Q.

Assertion: The expression $3x^4-4x^{\frac{3}{2}}+x^2$ is not a polynomial because the term $-4x^{\frac{3}{2}}$ contains a rational power of x.

Reason: The highest exponent(of the variable) in various terms of a polynomial in one variable is called its degree.

Which of the following is true?

1. Both Assertion and Reason are true, but the reason is not the correct explanation for the assertion.

2. Assertion is true and Reason is false.

3. Assertion is false and Reason is true.

4. Both Assertion and Reason are true and the reason is the correct explanation for the assertion.

Q. What are the polynomials which have 3 terms called?

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

Q. find the number of factors of polynomial f(x)=x^9-x

Q.

Find ab + 2ab.

1. 2ab

2. -ab

3. 3ab

4. ab

Q.

_{​​​​​​simplify}

_{(-3a^3/4*b^1/4)^4}

_{how to solve this?}

Q. Question 1(i)
Multiply the binomials:
(2x+5) and ( 4x-3)

Q. If x+1/x=4, then find the value of x^2[x^2+1/x^6]+[x^3+1/x^3].

Q.

When does the net area of a region equal the area of a​ region? When does a regions net area differ from a regions area?

Q. Question 42

In the question given below, fill in the blank to make the statement true:

The product of two polynomials is a ___

Q. Find the value of a which a polynomial 2x square+ax+2 has 1 as it 0 x=1

Q. Which of the following is a binomial?

1. $-7z$
2. $z^2-4y^2$
3. $x^{2}y-x{y}^2+y^2$
4. $12a-9ab+5b-3$

Q. Identify the region that represents x${}^2$.

1. 
2. 
3. 
4. 

Q.

Question 2
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories:
$x+y,1000,x+x^2+x^3+x^4,7+y+5x,2y-3y^2,$ $2y-3y^2+4y^3,5x-4y+3xy,4z-15z^2,$
$ab+bc+cd+da,pqr,p^{2}q+p{q}^2,2p+2q$

Q.

35xy + 45x + 5y² + 25xyz is a ______.

1. monomial

2. binomial

3. trinomial

4. polynomial

Q. How do you calculate the square root of $20$ divided by the square root of $15$?

Q.

(a+b+c)^2

Q. If the ratio of the polynomial ax cube+3bx square+3cx+d are in A.P.Prove that 2b cube -3abc + a square d=0

Q. 6xyz is a .

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

Q.

Is x_/2 a polynomial?

Q.

Degree of a constant polynomial is _____.

1. 0

2. Any natural number

3. 1

4. Not defined

Q. Multiply the quotients obtained by dividing $24(x^4{y}^3{z}^3+x^3{y}^3{z}^4+x^3{y}^4{z}^3)$ by $8x^3{y}^3{z}^3$ and $25xyz(6x^2+13x+5)$ by $5(3x+5)$.

1. $3xyz(x+y+z)(2x+1)$

2. $15xyz(x+y+z)(2x+1)$

3. $5xyz(x+y+z)(2x+1)$
4. $15\left(xyz{)}^2\right(x+y+z\left)\right(2x+1)$

Q. The sum of $11x^2-8x+4$ and $6x^2+7x-10$ is

1. $17x^2+x-6$
2. $17x^2-x-6$
3. $17x^2-x+6$
4. $17x^2+x+6$