Question

Which of the following is NOT a cubic polynomial?

• A. $p\left(x\right)=\frac{x^3}{3}$
• B. $p\left(x\right)=\frac{0x}{x}+3x^3$
• C. $p\left(x\right)=x^3-x^2$
• D. $p\left(x\right)=(x-1)(x+1)$

Answer 1

The correct option is D $p\left(x\right)=(x-1)(x+1)$

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 $3$.

option (D) $p\left(x\right)=(x-1)(x+1)=x^2-1$ hence it has degree $2$

It is NOT a cubic polynomial.