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anonymous
 one year ago
Paula used synthetic division to divide the polynomial f(x) by x + 1, as shown:
What is the value of f(–1)?
7
–2
1
–1
anonymous
 one year ago
Paula used synthetic division to divide the polynomial f(x) by x + 1, as shown: What is the value of f(–1)? 7 –2 1 –1

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0Sorry I had to read up a sec :) I sort of forgot synthetic lol The Remainder Theorem tells us that when you perform this division, the remainder will tell us the value of the function at that x value. Do you know how to find the remainder in this division diagram?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0think about what you compute using synthetic division: $$(2\cdot1+5)\cdot1+4=2\cdot(1)^25\cdot(1)+4=2x^25x+4$$ evaluated at \(x=1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the remainder (final) term in synthetic division gives you the value of the polynomial at that point; see the remainder theorem  if we divide a polynomial \(P\) by a divisor \(D\) and get the quotient \(Q\) with remainder \(R\) we have: $$P(x)=D(x)Q(x)+R(x)$$ if \(D\) has a zero at \(x=a\), then we see: $$P(a)=D(a)Q(a)+R(a)\\\implies P(a)=R(a)\text{ since }D(a)=0$$ so if we divide by a monomial \(D(x)=x+1\), the remainder \(R(x)\) will tell us the value at the zero of \(D\) (which is \(1\), since \(D(1)=0\)). see: $$P(1)=D(1)Q(1)+R(1)\\\implies P(1)=R(1)$$ so the remainder term givesu s what we want
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