QQuestionMathematics
QuestionMathematics
Determine all the zeros for the function f(2$)=(x^2 + 2x−8)(x−6).
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Step 1:: First, let's expand the given function using the distributive property (also known as FOIL for quadratic functions):
f(x) = x^3 - 6x^2 + 2x^2 - 12x - 8x + 48
Step 2:: Next, we combine like terms:
To find the zeros of this function, we need to find the roots of the equation $f(x) = 0$.
This can be done by factoring or using the rational root theorem.
Step 3:: Factoring by grouping, we get:
f(x) = x(x - 10)(x + 2) - 48
Step 4:: Now, we can set each factor equal to zero to find the zeros:
x + 2 = 0 \Rightarrow x = -2
Step 5:: Finally, we check for any extraneous solutions (which may have been introduced due to factoring), but since all the factors directly came from the original function, there are no extraneous solutions.
Final Answer
x = 1$, and $x = - 1$.
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