https://file.aiquickdraw.com/mathbot/file/1729783731661ybpj6wxg.jpg

Let's solve both questions by evaluating the given polynomials at the specified values of \( x \) and \( y \).

### Question 13:
Polynomial: 
\[
-7x^2 - 7y^2 - 2xy - 1
\]
We need to evaluate this polynomial for \( x = 4 \) and \( y = -1 \).

1. First, substitute \( x = 4 \) and \( y = -1 \) into the polynomial:
   \[
   -7(4^2) - 7((-1)^2) - 2(4)(-1) - 1
   \]
2. Simplify the terms:
   \[
   -7(16) - 7(1) - 2(4)(-1) - 1
   \]
   \[
   = -112 - 7 + 8 - 1
   \]
   \[
   = -112 - 7 + 8 - 1 = -112 - 7 + 7 = -112
   \]

The value of the polynomial for \( x = 4 \) and \( y = -1 \) is **-112**.

---

### Question 14:
Polynomial: 
\[
-6x^2 + y^2 + xy - 6
\]
We need to evaluate this polynomial for \( x = 4 \) and \( y = 6 \).

1. First, substitute \( x = 4 \) and \( y = 6 \) into the polynomial:
   \[
   -6(4^2) + (6^2) + (4)(6) - 6
   \]
2. Simplify the terms:
   \[
   -6(16) + 36 + 24 - 6
   \]
   \[
   = -96 + 36 + 24 - 6
   \]
   \[
   = -96 + 60 - 6 = -96 + 54 = -42
   \]

The value of the polynomial for \( x = 4 \) and \( y = 6 \) is **-42**.

---

Let me know if you'd like a further breakdown of these steps or explanations!

### Relative Questions:
1. What is the significance of the degree of a polynomial in relation to its behavior as \( x \) and \( y \) grow large?
2. How do negative values of \( x \) and \( y \) influence the overall polynomial evaluation?
3. What is the impact of mixed terms like \( 2xy \) on the structure of the polynomial?
4. How would you factor a polynomial like the ones given if necessary?
5. Can you express the polynomials in a factored form? If so, how?

### Tip:
Always double-check your substitutions when evaluating polynomials to avoid small mistakes that can affect the entire outcome.

Evaluate the polynomial -7x^2 - 7y^2 - 2xy - 1 for x = 4 and y = -1; Evaluate the polynomial -6x^2 + y^2 + xy - 6 for x = 4 and y = 6.

Learn how to evaluate the polynomials -7x^2 - 7y^2 - 2xy - 1 and -6x^2 + y^2 + xy - 6 by substituting x = 4 and y = -1, and x = 4 and y = 6 respectively. Follow a step-by-step breakdown of polynomial evaluation, useful for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation