Math  /  Algebra

QuestionUse the given zeros to write the complete factored form of f(x)f(x). f(x)=2x223x+66;f(x)=2 x^{2}-23 x+66 ; zeros: 112\frac{11}{2} and 6 f(x)=f(x)= \square (Type your answer in factored form. Use integers or fractions for any numbers

Studdy Solution
Verify the factored form by expanding:
f(x)=2(x112)(x6) f(x) = 2(x - \frac{11}{2})(x - 6)
First, expand the factors:
(x112)(x6)=x26x112x+112×6 (x - \frac{11}{2})(x - 6) = x^2 - 6x - \frac{11}{2}x + \frac{11}{2} \times 6
Combine like terms:
=x2(6+112)x+33 = x^2 - \left(6 + \frac{11}{2}\right)x + 33
=x2232x+33 = x^2 - \frac{23}{2}x + 33
Now, multiply by 2 2 :
f(x)=2(x2232x+33) f(x) = 2(x^2 - \frac{23}{2}x + 33)
=2x223x+66 = 2x^2 - 23x + 66
The expanded form matches the original polynomial, confirming the factored form is correct.
The complete factored form of f(x) f(x) is:
f(x)=2(x112)(x6) f(x) = 2(x - \frac{11}{2})(x - 6)

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