Question

Which of the following are not a cubic polynomial?

• A. $p\left(x\right)=x^3-3x^2+10$
• B. $p\left(x\right)=\frac{1}{3}{x}^2-6x+14$
• C. $p\left(x\right)=x^3-24x$
• D. $p\left(x\right)=x^2-2x+6$

Answer 1

Answer: (B), (D)

The correct options are
B $p\left(x\right)=\frac{1}{3}{x}^2-6x+14$
D $p\left(x\right)=x^2-2x+6$

The general form of cubic polynomial is $p\left(x\right)=a{x}^3+b{x}^2+cx+d$ where $x$ is a variable and $a,b,c,d$ are constants. The first term of this polynomial has power $3$, the second term of this polynomial has power $2$ and the third term of this polynomial has power $1$ and therefore, the degree of the polynomial is the largest exponent that is $3$.

But, in the polynomial $p\left(x\right)=x^2-2x+6$, the first term of this polynomial has power $2$, the second term of this polynomial has power $1$ and therefore, the degree of the polynomial is the largest exponent that is $2$.

Similarly in the polynomial $p\left(x\right)=\frac{1}{3}\times x^2-6x+14$,the first term of this polynomial has power $2$, the second term of this polynomial has power $1$ and therefore, the degree of the polynomial is the largest exponent that is $2$.

Hence, the polynomials in option B,D are not a cubic polynomials.