divide (5x3 -3x2) by x2 and write your answer in the form D=d×q+r
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Answer:
ose we wish to find the zeros of f(x)=x3+4x2−5x−14. Setting f(x)=0 results in the polynomial equation x3+4x2−5x−14=0. Despite all of the factoring techniques we learned in Intermediate Algebra, this equation foils us at every turn. If we graph f using the graphing calculator, we get
The graph suggests that the function has three zeros, one of which is x=2. It's easy to show that f(2)=0, but the other two zeros seem to be less friendly. Even though we could use the 'Zero' command to find decimal approximations for these, we seek a method to find the remaining zeros exactly. Based on our experience, if x=2 is a zero, it seems that there should be a factor of (x−2) lurking around in the factorization of f(x). In other words, we should expect that x3+4x2−5x−14=(x−2)q(x), where q(x) is some other polynomial. How could we find such a q(x), if it even exists? The answer comes from our old friend, polynomial division. Dividing x3+4x2−5x−14 by x−2 gives