To find the polynomial expression for [tex]\( A \)[/tex], we begin by defining [tex]\( A \)[/tex] as a polynomial in the variable [tex]\( x \)[/tex]. The polynomial is given in the form:
[tex]\[ A = 5x^3 - 4x^2 + 7x + 15 \][/tex]
Let's break down each term in the polynomial:
1. The first term is [tex]\( 5x^3 \)[/tex]:
- This term represents a cubic function with a coefficient of 5.
- It indicates that for any value of [tex]\( x \)[/tex], we need to cube the value and then multiply it by 5.
2. The second term is [tex]\( -4x^2 \)[/tex]:
- This term represents a quadratic function with a coefficient of -4.
- For any value of [tex]\( x \)[/tex], square the value and then multiply it by -4.
3. The third term is [tex]\( 7x \)[/tex]:
- This term is a linear function with a coefficient of 7.
- For any value of [tex]\( x \)[/tex], simply multiply it by 7.
4. The last term is a constant, [tex]\( 15 \)[/tex]:
- This term remains unchanged regardless of the value of [tex]\( x \)[/tex].
To write the polynomial from the combination of these four terms, we sum them together, maintaining the order of the terms with the highest degree first:
[tex]\[ A = 5x^3 - 4x^2 + 7x + 15 \][/tex]
Thus, the polynomial expression for [tex]\( A \)[/tex] is:
[tex]\[ \boxed{5x^3 - 4x^2 + 7x + 15} \][/tex]
