Exercise 13C
Question 1
1. Classify as constants or variables: $4,-8 y, \frac{3}{7},-8,9 x, a b, \frac{b x}{y}, 0, \frac{3 x^{2}}{2 z}$.
2. Write all the terms of the following algebraic expressions.
(i) $3 x+5 y-6 z$
(ii) $6 a^{2}+5 b^{2}-3 c d$
(iii) $7-9 x^{2}+5 y$
(iv) $4 a^{2}-7 b^{2}+2 a b-1$
3. Write down the algebraic expression whose terms are
(i) $4 a^{2},-2 b^{2},-3$
(ii) $7 x,-5,8 x^{2}$
(iii) $-3 p^{2}, 2 q^{2},-6 p q,-5$
(iv) $\frac{2}{3} x^{2},-\frac{4}{7} x y, 3 y^{2}$
4. Identify monomials, binomials and trinomials from the following.
(i) $2 m+3 n$
(ii) $a-5 b+7 c$
(iii) $\frac{2}{7} a^{2}$
(iv) $5 m^{2}-4$
(v) $7 a^{2}+2 b^{2}-4 a b$
(vi) $\frac{1}{2} x^{3}-y+z$
5. Write the coefficient of "a" in the following.
(i) $3 a$
(ii) pa
(iii) $-3 p a$
(iv) $4 a y^{2}$
(v) $-\frac{1}{5} a p$
6. Write the coefficient of
(i) $x$ in $-7 x y^{2}$
(ii) $m$ in $m x^{2}$
(iii) $x^{2} y$ in $\frac{5}{9} a x^{2} y$
(iv) $a$ in - $a$
7. Write down the numerical as well as the literal coefficient of the following monomials.
(i) $-12 x^{2} y$
(ii) $\frac{8}{15} a^{2} b c$
(iii) $-\frac{7}{9} a b c$
(iv) $-2 p q$
(v) $\frac{-3 x y}{7 z}$
(vi) $-6 x^{2} y^{2} z^{2}$
8. Identify the like terms in the following.
(i) $x^{2}, y^{2}, 2 x^{2}, z^{2}$
(ii) $3 x y, y z, 5 x, \frac{2}{7} y z$
(iii) $c a b^{2}, a^{2} b c, b^{2} a c, c^{2} a b, a b c, a c b^{2}$
9. Rearrange the factors so that literal factors are arranged alphabetically and follow the numerical factors.
(i) p3 q2r4s
(ii) $d e f 15 c$
(iii) $x 4 y z 2$
(iv) $5 w 2 t$
10. Which of the following algebraic expressions are polynomials?
(i) $x^{2}-\frac{1}{x^{2}}+2$
(ii) $\frac{3}{7} x^{2}-\frac{3}{7} x^{2}+3$
(iii) $81 x^{2}+4 x y-9 y^{2}-6$
(iv) $\frac{2}{x}+\frac{3}{x^{2}}-4 x^{2}-2 x+3$
(v) $8 x^{3}+7 x^{2}-12 x+4$
(vi) $p^{2}+p^{2} q-\frac{4 p}{q}+8$
11. Write down the degrees of the following polynomials.
(i) $a b+b c+c a$
(ii) $2+p^{2}$
(iii) $3 x^{2}-x^{4}$
(iv) $3 p^{2}+5 p^{3}+7 p^{5}$
(v) 4
(vi) $2 x^{2}+x y z+3 y^{3}$
(vii) $a^{2} b+a^{3} b^{2}+2 a b$
Multiple Choice Question (MCQ)
Tick (✔) the correct option.
12. A constant is a polynomial of degree
(a) 1
(b) 0
(c) cannot be determined
(d) None of these
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