Answer :
To correctly list the terms of the polynomial [tex]\(12x^3 - 6x^2 + 4x - 9\)[/tex], we will separate each individual term based on their coefficients and signs. A polynomial is a sum of terms, where each term is comprised of a coefficient (number), a variable part (like [tex]\(x\)[/tex]), and an exponent (the power to which the variable is raised).
Here are the steps to identify the terms:
1. Look at each part of the polynomial:
- The first term is [tex]\(12x^3\)[/tex], which consists of the coefficient 12.
- The second term is [tex]\(-6x^2\)[/tex], which consists of the coefficient -6.
- The third term is [tex]\(4x\)[/tex], with a coefficient of 4.
- The last term is a constant, [tex]\(-9\)[/tex].
2. List the terms with their respective signs:
- The full term [tex]\(12x^3\)[/tex] keeps the coefficient as 12.
- The full term [tex]\(-6x^2\)[/tex] includes the negative sign, hence the coefficient is -6.
- The full term [tex]\(4x\)[/tex] remains with a coefficient of 4.
- The constant term [tex]\(-9\)[/tex] is just -9.
By listing all terms, including their signs, we have: [tex]\(12x^3, -6x^2, 4x, -9\)[/tex].
Therefore, the correct selection that lists the terms: [tex]\(12x^3, -6x^2, 4x, -9\)[/tex].
Here are the steps to identify the terms:
1. Look at each part of the polynomial:
- The first term is [tex]\(12x^3\)[/tex], which consists of the coefficient 12.
- The second term is [tex]\(-6x^2\)[/tex], which consists of the coefficient -6.
- The third term is [tex]\(4x\)[/tex], with a coefficient of 4.
- The last term is a constant, [tex]\(-9\)[/tex].
2. List the terms with their respective signs:
- The full term [tex]\(12x^3\)[/tex] keeps the coefficient as 12.
- The full term [tex]\(-6x^2\)[/tex] includes the negative sign, hence the coefficient is -6.
- The full term [tex]\(4x\)[/tex] remains with a coefficient of 4.
- The constant term [tex]\(-9\)[/tex] is just -9.
By listing all terms, including their signs, we have: [tex]\(12x^3, -6x^2, 4x, -9\)[/tex].
Therefore, the correct selection that lists the terms: [tex]\(12x^3, -6x^2, 4x, -9\)[/tex].
