Math  /  Algebra

QuestionFactor the polynomial completely. P(x)=x2+49P(x)=\begin{array}{l} P(x)=x^{2}+49 \\ P(x)=\square \end{array} \square Find all its zeros. State the multiplicity of each zero. (Order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part.) x=x= \square with multiplicity x=x= \square with multiplicity \square

Studdy Solution
Determine the multiplicity of each zero. Since each factor appears once, each zero has a multiplicity of 1.
The factored form of the polynomial is:
P(x)=(x+7i)(x7i) P(x) = (x + 7i)(x - 7i)
The zeros of the polynomial are:
x=7i x = -7i with multiplicity 1
x=7i x = 7i with multiplicity 1

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