Write the degree of each of the following polynomials:
(i) $ 5 x^{3}+4 x^{2}+7 x $
(ii) $ 4-y^{2} $
(iii) $ 5 t-\sqrt{7} $
(iv) 3
To do:
We have to write the degree of each of the given polynomials.
Solution:
Degree of a polynomial:
A polynomial's degree is the highest or the greatest power of a variable in a polynomial.
Therefore,
(i) In $5 x^{3}+4 x^{2}+7 x^1$, the term $5x^3$ has a variable of power $3$, the term $4x^2$ has a variable of power $2$ and the term $7x^1$ has a variable of power $1$.
Therefore, the degree of the given polynomial is $3$.
(ii) In $4-y^{2}$, the term $4$ has a variable of power $0$ and the term $-y^2$ has a variable of power $2$.
Therefore, the degree of the given polynomial is $2$.
(iii) In $5 t-\sqrt{7}$, the term $5t^1$ has a variable of power $1$ and the term $-\sqrt7$ has a variable of power $0$.
Therefore, the degree of the given polynomial is $1$.
(iv) In $0=0\times x^0=0x^0$, the term $0x^0$ has a variable of power $0$.
Therefore, the degree of the given polynomial is $0$.
Related Articles
- Factorise:(i) \( 12 x^{2}-7 x+1 \)(ii) \( 2 x^{2}+7 x+3 \)(iii) \( 6 x^{2}+5 x-6 \)(iv) \( 3 x^{2}-x-4 \)
- Classify the following as linear, quadratic and cubic polynomials:(i) \( x^{2}+x \)(ii) \( x-x^{3} \)(iii) \( y+y^{2}+4 \)(iv) \( 1+x \)(v) \( 3 t \)(vi) \( r^{2} \)(vii) \( 7 x^{3} \)
- Which of the following expressions are not polynomials?:(i) $x^2+2x^{-2}$(ii) $\sqrt{ax}+x^2-x^3$(iii) $3y^3-\sqrt{5}y+9$(iv) $ax^{\frac{1}{2}}y^7+ax+9x^2+4$(v) $3x^{-3}+2x^{-1}+4x+5$
- Describe how the following expressions are obtained:$(i) 7 x y+5, (ii) x^{2} y, (iii) 4 x^{2}-5 x$.
- Which of the following expressions are polynomials? Which are not? Give reasons.(i) \( 4 x^{2}+5 x-2 \)(ii) \( y^{2}-8 \)(iii) 5(iv) \( 2 x^{2}+\frac{3}{x}-5 \)
- Determine which of the following polynomials has \( (x+1) \) a factor:(i) \( x^{3}+x^{2}+x+1 \)(ii) \( x^{4}+x^{3}+x^{2}+x+1 \)(iii) \( x^{4}+3 x^{3}+3 x^{2}+x+1 \)(iv) \( x^{3}-x^{2}-(2+\sqrt{2}) x+\sqrt{2} \)
- \Find $(x +y) \div (x - y)$. if,(i) \( x=\frac{2}{3}, y=\frac{3}{2} \)(ii) \( x=\frac{2}{5}, y=\frac{1}{2} \)(iii) \( x=\frac{5}{4}, y=\frac{-1}{3} \)(iv) \( x=\frac{2}{7}, y=\frac{4}{3} \)(v) \( x=\frac{1}{4}, y=\frac{3}{2} \)
- Add the following algebraic expressions(i) \( 3 a^{2} b,-4 a^{2} b, 9 a^{2} b \)(ii) \( \frac{2}{3} a, \frac{3}{5} a,-\frac{6}{5} a \)(iii) \( 4 x y^{2}-7 x^{2} y, 12 x^{2} y-6 x y^{2},-3 x^{2} y+5 x y^{2} \)(iv) \( \frac{3}{2} a-\frac{5}{4} b+\frac{2}{5} c, \frac{2}{3} a-\frac{7}{2} b+\frac{7}{2} c, \frac{5}{3} a+ \) \( \frac{5}{2} b-\frac{5}{4} c \)(v) \( \frac{11}{2} x y+\frac{12}{5} y+\frac{13}{7} x,-\frac{11}{2} y-\frac{12}{5} x-\frac{13}{7} x y \)(vi) \( \frac{7}{2} x^{3}-\frac{1}{2} x^{2}+\frac{5}{3}, \frac{3}{2} x^{3}+\frac{7}{4} x^{2}-x+\frac{1}{3} \) \( \frac{3}{2} x^{2}-\frac{5}{2} x-2 \)
- Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.(i) \( 4 x^{2}-3 x+7 \)(ii) \( y^{2}+\sqrt{2} \)(iii) \( 3 \sqrt{t}+t \sqrt{2} \)(iv) \( y+\frac{2}{y} \)(v) \( x^{10}+y^{3}+t^{50} \)
- Simplify the following :$( 3 x^2 + 5 x - 7 ) (x-1) - ( x^2 - 2 x + 3 ) (x + 4)$
- Find the following products:(i) $(x + 4) (x + 7)$(ii) $(x - 11) (x + 4)$(iii) $(x + 7) (x - 5)$(iv) $(x - 3) (x - 2)$(v) $(y^2 - 4) (y^2 - 3)$(vi) $(x + \frac{4}{3}) (x + \frac{3}{4})$(vii) $(3x + 5) (3x + 11)$(viii) $(2x^2 - 3) (2x^2 + 5)$(ix) $(z^2 + 2) (z^2 - 3)$(x) $(3x - 4y) (2x - 4y)$(xi) $(3x^2 - 4xy) (3x^2 - 3xy)$(xii) $(x + \frac{1}{5}) (x + 5)$(xiii) $(z + \frac{3}{4}) (z + \frac{4}{3})$(xiv) $(x^2 + 4) (x^2 + 9)$(xv) $(y^2 + 12) (y^2 + 6)$(xvi) $(y^2 + \frac{5}{7}) (y^2 - \frac{14}{5})$(xvii) $(p^2 + 16) (p^2 - \frac{1}{4})$
- Subtract:(i) $-5xy$ from $12xy$(ii) $2a^2$ from $-7a^2$(iii) \( 2 a-b \) from \( 3 a-5 b \)(iv) \( 2 x^{3}-4 x^{2}+3 x+5 \) from \( 4 x^{3}+x^{2}+x+6 \)(v) \( \frac{2}{3} y^{3}-\frac{2}{7} y^{2}-5 \) from \( \frac{1}{3} y^{3}+\frac{5}{7} y^{2}+y-2 \)(vi) \( \frac{3}{2} x-\frac{5}{4} y-\frac{7}{2} z \) from \( \frac{2}{3} x+\frac{3}{2} y-\frac{4}{3} z \)(vii) \( x^{2} y-\frac{4}{5} x y^{2}+\frac{4}{3} x y \) from \( \frac{2}{3} x^{2} y+\frac{3}{2} x y^{2}- \) \( \frac{1}{3} x y \)(viii) \( \frac{a b}{7}-\frac{35}{3} b c+\frac{6}{5} a c \) from \( \frac{3}{5} b c-\frac{4}{5} a c \)
- Simplify the expressions and find the value if $x$ is equal to $2$$(i)$. $x+7+4(x-5)$$(ii)$. $3(x+2)+5x-7$$(iii)$. $6x+5(x-2)$$(iv)$. $4(2x-1)+3x+11$
- Identify polynomials in the following:\( f(x)=4 x^{3}-x^{2}-3 x+7 \)
- Draw the graph of each of the following linear equations in two variables:(i) \( x+y=4 \)(ii) \( x-y=2 \)(iii) \( y=3 x \)(iv) \( 3=2 x+y \).
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies