Asked by pakyo
Which of the following polynomials can approximate the expression (4x3+5)(3x6−8x2)2x2+4x3+13 using first and last terms only?(1 point) Responses 12x9+…13 12 x to the 9th power plus dot dot dot 13 6x7+…−7 6 x to the 7th power plus dot dot dot minus 7 4x3+…13 4 x cubed plus dot dot dot 13 6x7+…4x3
Answers
Answered by
GPT-4o mini
To approximate the expression \( (4x^3 + 5)(3x^6 - 8x^2) + 2x^2 + 4x^3 + 13 \) using only the first and last terms, we first need to identify those terms.
1. **Identifying the first terms:**
- The leading term of \( (4x^3)(3x^6) = 12x^9 \).
2. **Identifying the constant term:**
- The constant term comes from \( 5 \) (from \( 4x^3 + 5 \)) multiplied by the remaining terms evaluated at their constant portions. In this case, we focus on \( 2x^2 + 4x^3 + 13 \), where the constant term is \( 13 \).
Putting these together:
- The first term of the polynomial is \( 12x^9 \).
- The last term (constant term) is \( 13 \).
Thus, the polynomial that can approximate the expression, considering only the first and last terms, is:
**12x^9 + ... + 13**
So the correct response is:
**12x^9 + ... + 13**
1. **Identifying the first terms:**
- The leading term of \( (4x^3)(3x^6) = 12x^9 \).
2. **Identifying the constant term:**
- The constant term comes from \( 5 \) (from \( 4x^3 + 5 \)) multiplied by the remaining terms evaluated at their constant portions. In this case, we focus on \( 2x^2 + 4x^3 + 13 \), where the constant term is \( 13 \).
Putting these together:
- The first term of the polynomial is \( 12x^9 \).
- The last term (constant term) is \( 13 \).
Thus, the polynomial that can approximate the expression, considering only the first and last terms, is:
**12x^9 + ... + 13**
So the correct response is:
**12x^9 + ... + 13**