Certainly! Let's consider the given polynomial: [tex]\( 3x^3 - 2x + 7 \)[/tex].
1) How many terms does this polynomial have?
A polynomial is an expression consisting of variables (also called indeterminates), coefficients, and non-negative integer exponents of those variables. The terms in a polynomial are typically separated by plus (+) or minus (−) signs.
Let's break down the polynomial [tex]\( 3x^3 - 2x + 7 \)[/tex] into its individual terms:
- The first term is [tex]\( 3x^3 \)[/tex].
- The second term is [tex]\( -2x \)[/tex].
- The third term is [tex]\( 7 \)[/tex].
So, there are three terms in this polynomial.
Answer: The polynomial has [tex]\( 3 \)[/tex] terms.
2) What is the coefficient of the second term?
The coefficient of a term in a polynomial is the numerical factor in front of the variable part of the term. If there is no variable, the term itself is the coefficient.
For the polynomial [tex]\( 3x^3 - 2x + 7 \)[/tex], let's identify the second term:
- The first term is [tex]\( 3x^3 \)[/tex].
- The second term is [tex]\( -2x \)[/tex].
The coefficient of the second term ([tex]\( -2x \)[/tex]) is the number in front of the variable [tex]\( x \)[/tex], which is [tex]\( -2 \)[/tex].
Answer: The coefficient of the second term is [tex]\( -2 \)[/tex].
