Question

Which among the following algebraic expressions does not contain a constant term?

• A. $8x+7y+6z$
• B. $2x^3+9y^4+5$
• C. $27x^4+91z^4+84$
• D. $7a^2+6b^2-42$

Answer 1

The correct option is A $8x+7y+6z$

$\underset{–}{\text{Constant Term}:}$
In mathematics, a constant term is a term in an algebraic expression that does not contain any variables and therefore is constant.

For example, in the quadratic polynomial $x^2+2x+3,$ $3$ is a constant term.

$\underset{–}{\text{Note}:}$
After like terms are combined, an algebraic expression will have at most one constant term.

$\underset{–}{\text{Need to Identify:}}$
The algebraic expression that does not contain a constant

$\bullet$ (a.) $\underset{–}{8x+7y+6z}:$


$\bullet$ Variable terms: $8x$, $7y$ and $6z$
$\bullet$ Constant term: No constant term
$\underset{–}{}$


$\bullet$ (b.) $\underset{–}{2x^3+9y^4+5}:$


$\bullet$ Variable terms: $2x^3$ and $9y^4$
$\bullet$ Constant term: $5$
$\underset{–}{}$


$\bullet$ (c.) $\underset{–}{27x^4+91z^4+84}:$


$\bullet$ Variable terms: $27x^4$ and $91z^4$
$\bullet$ Constant term: $84$
$\underset{–}{}$


$\bullet$ (d.) $\underset{–}{7a^2+6b^2-42}:$


$\bullet$ Variable terms: $7a^2$ and $6b^2$
$\bullet$ Constant term: $-42$

Therefore, option (a.) is the correct choice as it does not contain any constant term.