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Four is a zero of the equation x^3+3x^2−18x−40=0.

Which factored form is equivalent to the equation?

A.  (x+2)(x−√4)(x+√4)=0

B.  (x−4)(x+2)(x+5)=0

C.  (x+4)(x+2)(x+5)=0

D.  (x−4)(x+4)(x+5)=0

Sep 25, 2018
edited by Guest  Sep 25, 2018

#1
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if four is a zero then (x-4) is a factor

$$\text{so we divide }x^3+3x^2 - 18x-40 \text{ by } (x-4) \\ \text{to determine what the other factors might be.} \\ \dfrac{x^3 + 3x^2 - 18 x - 40}{x-4}= x^2+7 x+10$$

$$\text{This quotient is easy enough to factor as }\\ x^2 + 7x+10 = (x+5)(x+2) \\ \text{and thus}\\ x^3+ 3x^2-18x-40 = (x-4)(x+2)(x+5) \\ \text{this is choice B}$$

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Sep 25, 2018

#1
+5776
+1

if four is a zero then (x-4) is a factor

$$\text{so we divide }x^3+3x^2 - 18x-40 \text{ by } (x-4) \\ \text{to determine what the other factors might be.} \\ \dfrac{x^3 + 3x^2 - 18 x - 40}{x-4}= x^2+7 x+10$$

$$\text{This quotient is easy enough to factor as }\\ x^2 + 7x+10 = (x+5)(x+2) \\ \text{and thus}\\ x^3+ 3x^2-18x-40 = (x-4)(x+2)(x+5) \\ \text{this is choice B}$$

Rom Sep 25, 2018