Question

Which among the following correctly represents a polynomial expression and polynomial equation in the variable $x$?

• A. Polynomial Expression $=10+9m$
  Polynomial Equation:
  $7+8m=15$
• B. Polynomial Expression $=15+16x$
  Polynomial Equation:
  $8+9y=7$
• C. Polynomial Expression $=2x+3$
  Polynomial Equation:
  $4x+9=36$
• D. Polynomial Expression $=5x+1$
  Polynomial Equation:
  $9p+3=17$

Answer 1

The correct option is C Polynomial Expression $=2x+3$

Polynomial Equation:
$4x+9=36$
$\underset{–}{\text{Expression}:}$
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
For example, $2x+3,x{y}^2+5x$ etc.

$\underset{–}{\text{Equation}:}$
An equation is made up of two expressions connected by an equal sign.
For example, $2x^2+7x=5x+2,x^2=4$ etc.

In option (a.), we have:
Polynomial Expression $=10+9m$
Polynomial Equation:
$7+8m=15$

It contains a polynomial expression in $m$ and a polynomial equation in $m$.

In option (b.), we have:
Polynomial Expression $=15+16x$
Polynomial Equation:
$8+9y=7$

It contains a polynomial expression in $x$ and a polynomial equation in $y$.

In option (c.), we have:
Polynomial Expression $=2x+3$
Polynomial Equation:
$4x+9=36$

It contains a polynomial expression in $x$ and a polynomial equation in $x$.

In option (d.), we have:
Polynomial Expression $=5x+1$
Polynomial Equation:
$9p+3=17$

It contains a polynomial expression in $x$ and a polynomial equation in $p$.

Therefore, option (c.) is the correct answer as it contains both the polynomial expression and the polynomial equation in the variable $x$.