Answer :
To determine which of the given terms is a quadratic term, we need to understand what a quadratic term is. A quadratic term has the form [tex]\( ax^2 \)[/tex], where [tex]\( a \)[/tex] is a constant and [tex]\( x \)[/tex] is a variable raised to the power of 2.
Let's examine each option:
1. [tex]\( 8x^2 \)[/tex]: This term is in the form of [tex]\( ax^2 \)[/tex]. Here, [tex]\( a = 8 \)[/tex] and the variable [tex]\( x \)[/tex] is squared. Therefore, this is a quadratic term.
2. 2: This is a constant term. It doesn't contain a variable, so it cannot be a quadratic term.
3. [tex]\(-19x^3\)[/tex]: This term has a variable [tex]\( x \)[/tex] raised to the power of 3, not 2. Therefore, it is not a quadratic term; it's a cubic term.
4. [tex]\( 5x \)[/tex]: This term has the variable [tex]\( x \)[/tex] raised to the power of 1. It is a linear term, not a quadratic term.
Based on the explanations above, the term [tex]\( 8x^2 \)[/tex] is the only quadratic term among the options.
Let's examine each option:
1. [tex]\( 8x^2 \)[/tex]: This term is in the form of [tex]\( ax^2 \)[/tex]. Here, [tex]\( a = 8 \)[/tex] and the variable [tex]\( x \)[/tex] is squared. Therefore, this is a quadratic term.
2. 2: This is a constant term. It doesn't contain a variable, so it cannot be a quadratic term.
3. [tex]\(-19x^3\)[/tex]: This term has a variable [tex]\( x \)[/tex] raised to the power of 3, not 2. Therefore, it is not a quadratic term; it's a cubic term.
4. [tex]\( 5x \)[/tex]: This term has the variable [tex]\( x \)[/tex] raised to the power of 1. It is a linear term, not a quadratic term.
Based on the explanations above, the term [tex]\( 8x^2 \)[/tex] is the only quadratic term among the options.
