Question

What are the degree and zeros of the polynomial f(x) = (x - 1)(x + 1)?

a. Degree 2; zeros 1, -1
b. Degree 3; zeros 1, 3
c. Degree 1; zeros 1, -1
d. Degree 1; zeros -1, 3

Answer 1

The answer of the given equation is "the degree and zeros of the polynomial f(x) = (x - 1)(x + 1)" is a. Degree 2; zeros 1, -1

Step-by-step explanation:

The polynomial
`\(f(x) = (x - 1)(x + 1)\)` can be expanded to
`\(f(x) = x^2 - 1\).`The degree of a polynomial is the highest power of the variable present. In this case, the highest power of
`\(x\)` is 2, so the degree is 2.

To find the zeros, set
`\(f(x)\)` equal to zero and solve for
`\(x\):`

`\[x^2 - 1 = 0\]`

This equation has solutions when
`\(x = 1\)` and
`\(x = -1\).` Therefore, the zeros of the polynomial are 1 and -1.

In summary, the correct answer is a. Degree 2; zeros 1, -1.