Certainly! Let's break down the polynomial [tex]\( 8x^4 - 2x \)[/tex] and identify the coefficients and exponents for each term.
A polynomial term typically takes the form [tex]\( ax^n \)[/tex], where [tex]\( a \)[/tex] is the coefficient and [tex]\( n \)[/tex] is the exponent.
1. First Term: [tex]\( 8x^4 \)[/tex]
- Coefficient: The coefficient [tex]\( a \)[/tex] is the number in front of the variable [tex]\( x \)[/tex]. For the term [tex]\( 8x^4 \)[/tex], the coefficient is [tex]\( 8 \)[/tex].
- Exponent: The exponent [tex]\( n \)[/tex] is the power to which the variable [tex]\( x \)[/tex] is raised. For the term [tex]\( 8x^4 \)[/tex], the exponent is [tex]\( 4 \)[/tex].
2. Second Term: [tex]\( -2x \)[/tex]
- Coefficient: The coefficient [tex]\( a \)[/tex] is the number in front of the variable [tex]\( x \)[/tex]. For the term [tex]\( -2x \)[/tex], the coefficient is [tex]\( -2 \)[/tex].
- Exponent: The exponent [tex]\( n \)[/tex] is the power to which the variable [tex]\( x \)[/tex] is raised. For the term [tex]\( -2x \)[/tex], the exponent is [tex]\( 1 \)[/tex] because [tex]\( x \)[/tex] is the same as [tex]\( x^1 \)[/tex].
So, based on these observations:
- For the term [tex]\( 8x^4 \)[/tex]: Coefficient is [tex]\( 8 \)[/tex], and exponent is [tex]\( 4 \)[/tex].
- For the term [tex]\( -2x \)[/tex]: Coefficient is [tex]\( -2 \)[/tex], and exponent is [tex]\( 1 \)[/tex].
Summary:
- The coefficients are [tex]\( 8 \)[/tex] and [tex]\( -2 \)[/tex].
- The exponents are [tex]\( 4 \)[/tex] and [tex]\( 1 \)[/tex].
The correct choice from the given options is:
- The coefficients are 8 and -2. The exponents are 4 and 1.
