1. **Problem:** Given the polynomial function $p(x) = (3x+2)(1-5x)(1-x^2)$, determine which statement about $p(x)$ is correct. 2. **Step 1: Find the constant term of $p(x)$.** - The constant term is found by multiplying the constant terms of each factor. - Constants: from $(3x+2)$ is 2, from $(1-5x)$ is 1, from $(1-x^2)$ is 1. - So, constant term = $2 \times 1 \times 1 = 2$. 3. **Step 2: Find the leading coefficient of $p(x)$.** - Leading term comes from multiplying the highest degree terms in each factor. - Highest degree terms: $3x$ from $(3x+2)$, $-5x$ from $(1-5x)$, and $-x^2$ from $(1-x^2)$. - Multiply: $3x \times (-5x) \times (-x^2) = 3 \times (-5) \times (-1) \times x \times x \times x^2 = 15x^4$. - Leading coefficient is 15. 4. **Step 3: Check if $p(x)$ is a polynomial over integers.** - All coefficients in the factors are integers. - Multiplying polynomials with integer coefficients results in a polynomial with integer coefficients. - So, $p(x)$ is a polynomial over integers. 5. **Step 4: Find the degree of $p(x)$.** - Degree is sum of degrees of each factor. - Degrees: 1 from $(3x+2)$, 1 from $(1-5x)$, 2 from $(1-x^2)$. - Total degree = $1 + 1 + 2 = 4$. 6. **Conclusion:** - Constant term is 2, not -2 (so A is false). - Leading coefficient is 15, not -15 (so B is false). - $p(x)$ is a polynomial over integers (C is true). - Degree is 4, not 3 (D is false). **Final answer:** C. p(x) is a polynomial over integer.