Question

Which of the following polynomials does not has a degree $3$ ?

• A. $2x^3–5x^2+ax+b=0$
• B. $6x^3–11x^2+kx=20$
• C. $3x+8=4$
• D. $\sqrt[3]{x^2}=x$

Answer 1

The correct option is C

$3x+8=4$

Explanation for the correct option:

The polynomials that has a variable with the highest exponent of $3$ has a degree $3$.

For example: $6x^3–11x^2+5x-20=0$

Option (C)

$3x+8=4$ doesn't have a variable with exponent $3$. Its highest variable $x$has exponent $1$.

Hence, $3x+8=4$ doesn't have a degree $3$.

Explanation for the incorrect options:

Option (A):

$2x^3–5x^2+ax+b=0$ has a variable with exponent $3$.

Option (B):

$6x^3–11x^2+kx=20$ has a variable with exponent $3$

Option (D):

$$\begin{gathered} \sqrt[3]{x^2}=x \\ \Rightarrow {\left(\sqrt[3]{x^2}\right)}^3=x^3[Takingcubebothside] \\ \Rightarrow x^2=x^3[\because y\times x=y] \end{gathered}$$

$x^2=x^3$ has a variable with exponent $3$

Hence, option C is correct.