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Practice each question, then open the answer or worked solution.
An algebraic expression containing three terms is called a
(a) monomial (b) binomial (c) trinomial (d) All of these
Solution:-
(c) trinomial
Expression with three unlike terms is called a ‘Trinomial’.
Number of terms in the expression 3x2y – 2y2z – z2x + 5 is
(a) 2 (b) 3 (c) 4 (d) 5
Solution:-
(c) 4
In the given expression there are 4 terms.
The terms of expression 4x2 – 3xy are:
(a) 4x2 and –3xy (b) 4x2 and 3xy
(c) 4x2 and –xy (d) x2 and xy
Solution:-
(a) 4x2 and –3xy
A term is the product of factors.
Factors of –5x2 y2 z are
(a) – 5 × x × y × z (b) – 5 × x2 × y × z
(c) – 5 × x × x × y × y × z (d) – 5 × x × y × z2
Solution:-
(c) – 5 × x × x × y × y × z
Factors may be numerical as well as algebraic (literal).
Coefficient of x in – 9xy2z is
(a) 9yz (b) – 9yz (c) 9y2z (d) – 9y2z
Solution:-
(d) – 9y2z
Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.
Which of the following is a pair of like terms?
(a) –7xy2z, – 7x2yz (b) – 10xyz2, 3xyz2
(c) 3xyz, 3x2y2z2 (d) 4xyz2, 4x2yz
Solution:-
(b) – 10xyz2, 3xyz2
The terms having the same algebraic factors are called like terms.
Identify the binomial out of the following:
(a) 3xy2 + 5y – x2y (b) x2y – 5y – x2y
(c) xy + yz + zx (d) 3xy2 + 5y – xy2
Solution:-
(d) 3xy2 + 5y – xy2
Expression with two unlike terms is called a ‘Binomial’.
The expression 3xy2 + 5y – xy2 is further simplified as,
= 3xy2 + 5y – xy2
= (3xy2 – xy2) + 5y
= 2xy2 + 5y
The sum of x4 – xy + 2y2 and –x4 + xy + 2y2 is
(a) Monomial and polynomial in y (b) Binomial and Polynomial
(c) Trinomial and polynomial (d) Monomial and polynomial in x
Solution:-
(a) Monomial and polynomial in y
Consider the given equation, x4 – xy + 2y2 and –x4 + xy + 2y2
Sum of two expressions = (x4 – xy + 2y2) + (–x4 + xy + 2y2)
= x4 – xy + 2y2 – x4 + xy + 2y2
= (x4 – x4)+ (-xy + xy) + (2y2 + 2y2)
= 0 + 0 + 4y2
= 4y2
The subtraction of 5 times of y from x is
(a) 5x – y (b) y – 5x (c) x – 5y (d) 5y – x
Solution:-
(c) x – 5y
– b – 0 is equal to
(a) –1 × b (b) 1 – b – 0 (c) 0 – (–1) × b (d) – b – 0 – 1
Solution:-
(a) –1 × b
– b – 0 is equal to = -b