Explanation Result used: The Factor Theorem: “For a polynomial f ( x ) , if f ( c ) = 0 , then x − c is a factor of f ( x ) ”. “ Zero-Factor Property: If a and b are real numbers and if ab = 0 then a = 0 or b = 0 That is, if the product of two numbers is 0, then at least one of the numbers must be 0.”. Calculation: Consider the polynomial function f ( x ) = x 3 + 4 x 2 + x − 6 . Use the above result, to find the zeros of a polynomial function as follows. Assume the factor as x − 1 . Check f ( 1 ) = 0 or not, in order to check x − 1 is factor of the given polynomial function. 1 1 4 1 − 6 1 5 6 _ 1 5 6 0 By the result stated above, x − 1 is the factor of the polynomial function and the quotient is x 2 + 5 x + 6

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Author: BITTINGER

Publisher: PEARSON

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Chapter 4.3, Problem 39E

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To factor: The polynomial function f(x)=x3+4x2+x−6 and then solve the equation f(x)=0.

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Chapter 4.3, Problem 38E

Chapter 4.3, Problem 40E

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To factor: The polynomial function f ( x ) = x 3 + 4 x 2 + x − 6 and then solve the equation f ( x ) = 0 .

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To factor: The polynomial function f(x)=x3+4x2+x−6 and then solve the equation f(x)=0.

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