Question

question 1 write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros of -2, -1, 2, and 2. y(x) = question help: video read written example message instructor submit question

Explanation:

Step1: Recall factor - zero relationship

If \(r\) is a zero of a polynomial, then \((x - r)\) is a factor of the polynomial.

Step2: Write factors for given zeros

For \(r=-2\), the factor is \((x + 2)\); for \(r = - 1\), the factor is \((x+1)\); for \(r = 2\) (which appears twice), the factors are \((x - 2)(x - 2)\).

Step3: Form the polynomial

The polynomial \(y(x)\) with a leading - coefficient of 1 is the product of its factors, so \(y(x)=(x + 2)(x + 1)(x - 2)^2\).

Answer:

\(y(x)=(x + 2)(x + 1)(x - 2)^2\)