Question

Classify the following polynomials based on their degree.
(i)$p\left(x\right)=3$

(ii) $p\left(y\right)=\frac{5}{2}{y}^2+1$

(iii)$p\left(x\right)=2x^3-x^2+4x+1$

(iv)$p\left(x\right)=3x^2$
(v)$p\left(x\right)=x+3$

(vi) $p\left(x\right)=-7$

(vii) $p\left(x\right)=x^3+1$

(viii) $p\left(x\right)=5x^2-3x+2$

(ix)$p\left(x\right)=4x$
(x) $p\left(x\right)=\frac{3}{2}$

(xi) $p\left(x\right)=\sqrt{3}x+1$

(xii) $p\left(y\right)=y^3+3y$

Answer 1

$p\left(x\right)=3,p\left(x\right)=-7,p\left(x\right)=\frac{3}{2}$ are constant polynomials.

$p\left(x\right)=x+3,p\left(x\right)=4x,p\left(x\right)=\sqrt{3}x+1$ are linear polynomials, since the highest degree of the variable x is one.

$p\left(x\right)=5x^2-3x+2,p\left(y\right)=\frac{5}{2}{y}^2+1,p\left(x\right)=3x^2$ are quadratic polynomials, since the highest degree of the variable is two.

$p\left(x\right)=2x^3-x^2+4x+1,p\left(x\right)=x^3+1,p\left(y\right)=y^3+3y$ are cubic polynomials, since the highest degree of the variable is three.