Thts question: 10 point(s) possibl

For the following polynomial function, find (A) the degree of the polynomial (B) all -intercepts, and © the -intercept

(A) The degree of the polynomial is
(B) The -intercept(s) is/are
(Use a comma to separate answers as needed Type integers or fractions)
© The intercopt is
(Trpe an integes or a fraction)

Ask by Gray Howell. in the United States

Jan 03,2025

Question

Thts question: 10 point(s) possibl

For the following polynomial function, find (A) the degree of the polynomial (B) all -intercepts, and © the -intercept

(A) The degree of the polynomial is
(B) The -intercept(s) is/are
(Use a comma to separate answers as needed Type integers or fractions)
© The intercopt is
(Trpe an integes or a fraction)

Ask by Gray Howell. in the United States

Jan 03,2025

UpStudy AI · Accepted Answer

Let's analyze the polynomial function $$ t(x) = x^{2} - x - 6 $$ to find the requested information.

### (A) Degree of the Polynomial
The **degree** of a polynomial is the highest power of the variable $$ x $$ in the expression.

- In $$ t(x) = x^{2} - x - 6 $$, the highest power of $$ x $$ is **2**.

**Answer:**  
The degree of the polynomial is $$ \boxed{2} $$.

---

### (B) $$ x $$-Intercept(s)
The $$ x $$-intercepts occur where the polynomial equals zero, i.e., $$ t(x) = 0 $$.

1. **Set the polynomial equal to zero:**
   $$
   x^{2} - x - 6 = 0
   $$
2. **Factor the quadratic equation:**
   $$
   (x - 3)(x + 2) = 0
   $$
3. **Solve for $$ x $$:**
   $$
   x - 3 = 0 \quad \Rightarrow \quad x = 3
   $$
   $$
   x + 2 = 0 \quad \Rightarrow \quad x = -2
   $$

**Answer:**  
The $$ x $$-intercepts are $$ \boxed{3, -2} $$.

---

### (C) $$ y $$-Intercept
The $$ y $$-intercept occurs where $$ x = 0 $$.

1. **Substitute $$ x = 0 $$ into the polynomial:**
   $$
   t(0) = (0)^{2} - (0) - 6 = -6
   $$

**Answer:**  
The $$ y $$-intercept is $$ \boxed{-6} $$.
**Polynomial Analysis:** - **Degree:** 2 - **$$ x $$-Intercepts:** 3, -2 - **$$ y $$-Intercept:** -6

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