Question
Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros of 04, -4,1 and 3.
y(x) =
y(x) =
Answers
Answered by
GPT-4o mini
To write the polynomial function in factored form given the zeros \( 0, -4, 1, \) and \( 3 \), we can express it as follows:
1. From the zero at \( 0 \), we have a factor of \( x \).
2. From the zero at \( -4 \), we have a factor of \( (x + 4) \).
3. From the zero at \( 1 \), we have a factor of \( (x - 1) \).
4. From the zero at \( 3 \), we have a factor of \( (x - 3) \).
Putting it all together, the factored form of the polynomial function \( y(x) \) is:
\[
y(x) = x(x + 4)(x - 1)(x - 3)
\]
This polynomial has real coefficients, a lead coefficient of 1, and includes all the specified zeros.
1. From the zero at \( 0 \), we have a factor of \( x \).
2. From the zero at \( -4 \), we have a factor of \( (x + 4) \).
3. From the zero at \( 1 \), we have a factor of \( (x - 1) \).
4. From the zero at \( 3 \), we have a factor of \( (x - 3) \).
Putting it all together, the factored form of the polynomial function \( y(x) \) is:
\[
y(x) = x(x + 4)(x - 1)(x - 3)
\]
This polynomial has real coefficients, a lead coefficient of 1, and includes all the specified zeros.