Binomial

Q. Question 1

The product of a monomial and a binomial is a
a) monomial
b) binomial
c) trinomial
d) None of these

Q.

Identify the like and unlike terms in $4xy,8x^2$ and $3yx$.

1. Like: $4xy,8x^2$

2. Like: $4xy,3yx$

3. Unlike: $4xy,8x^2$

4. Unlike: $3yx,8x^2$

Q. Question 7

Which of the following is a binomial?
a) $7\times a+a$
b) $6a^2+7b+2c$
c) $4a\times 3b\times 2c$
d) $6(a^2+b)$

Q. Which of the following algebraic expressions is/are binomial expression(s)?

1. $9x+6y$
2. $7-4$
3. $2x+5-2y$
4. $x^{2}y+6xy$

Q. State True or False:
On subtracting $-3x^3+4x^2-5x+6$ from $3x^3-4x^2+5x-6$, the answer is $6x^3-8x^2+10x-12$.

1. True
2. False

Q.

Give three examples of the expressions:

(i) containing one variable

(ii) containing two variables

(iii) containing two terms. [4 MARKS]

Q.

Write the given statement in the form of algebraic expression and write whether it is monomial, binomial or trinomial: Two times $q$ subtracted from cube of $q$.

Q.

State whether the following expression is monomial, binomial, or trinomial.

$df+fg-1$

Q.

Find the product of algebraic expressions $\frac{2x}{7}$ and $\frac{3y}{5}$

1. $\frac{6x}{35}$

2. $\frac{6y}{35}$

3. $\frac{6xy}{35}$

4. $\frac{xy}{35}$

Q.

‘p’ and ‘q’ are the zeroes of the polynomial $a{x}^2+bx+c=0$.

$(x-p)$ and $(x-q)$ are the only factors of the expression $a{x}^2+bx+c$,

The values of $a$ and $b$ are:

1. -1, -(p + q)

2. 1, p + q

3. 1, -(p+q)

4. None of these

Q. Which of the following is a binomial expression?

1. 105a+105b
2. 𝑥𝑦𝑧
3. m+n+2
4. -9

Q.

A polynomial of degree 1 is called a __ polynomial.

Q. Which of the following expressions are binomials with 3 variables?

1. $3x+5xy$
2. $6xz+3z^3$
3. $2ab+3bc$
4. $2a^2+3b^{2}c$

Q. Simplify $(2x+1)(x-3)$.

Q. Which of the following is a binomial in $y$ ?

1. $y^2+\sqrt{2}$
2. $y+\frac{1}{y}+2$
3. $\sqrt{y}+\sqrt{2}y$
4. $y\sqrt{y}+1$

Q. Out of the following algebraic expressions, identify the binomial.

1. $3a\times 2b\times c$
2. $9a+a$
3. $6b^2+5a+c$
4. $5(a^2+b)$

Q.

‘-p’ and ‘q’ are the zeroes of the polynomial
$x^2–bx+c$.
The zeroes of the polynomial $x^2–bxy+c{y}^2$ are

1. None of these

2. -py, qy

3. py, -qy

4. py, qy

Q. Justify the following statement with examples :
The degree of a binomial can be more than two.

Q.

How many unlike terms does a binomial have?

1. $1$

2. $2$

3. $3$

4. $0$

Q.

The sum of $-5pq+5$, $12pq+2$, $7pq-8$, and $-2pq-5$ is ___________.

Q.

1. True
2. False

Q. Identify monomials, binomials, and trinomials from the following algebraic expressions:
$-3+7x^2$

Q.

Which of the following is a binomial?

1. $9\times a+a$

2. $3a\times 2b\times c$

3. $6b^2+5a+c$​

4. $5(a^2+b)$

Q. Pick the binomial with sum of the coefficients equal to 10.

1. 3x + 4y + 3z
2. 12p - 2q
3. 2m + 7n
4. 4x - y + 7

Q. State True or False:
On subtracting $-2x^{2}y+3x{y}^2$ from $8x^{2}y$, the answer is $10x^{2}y-3x{y}^2$.

1. True
2. False

Q. If the height of the triangle is $\sqrt{3}$ times of its base, then find the polynomial which represents the area of the triangle.

Q. Let $p$ and $q$ be the degree and the number of zeros of the polynomial $g\left(x\right)=x^2-6x+9$ then find $p+q-pq$

Q. Which of the following is binomal?

1. $3x+1$
2. $3x$
3. $x^2+x+2$
4. None of the above

Q. Which of the following is a binomial?

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

Q. Which of the following is a monomial?

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