- Yes! Deg, there is. This leftover is called a remainder!
- But Ms. Poly there's something leftover
- Well Ree, yes there is its called the remainder theorem. Lets turn to the board now.
- The Remainder theorem states that when polynomial p(x) is divided by x-a, the remainder is p(a).
- But there has to be an easier way to find the remainder! I always feel bad for the remainder when doing long division.
- Try This Problem: What is the remainder when 5x^2 + 5x +45 is divided by x-7.Work: P(7)= 5(7)^2 +5(7)-45= ?
- That's right Nomial!
- So the remainder is 235
- The Next Day
- Do Now: Find the remainder when x^3+5x^2 -26x-120 is divided by x-5.
- No that's correct! The remainder is zero, which means x-5 is a factor of p(x)
- I got zero for the remainder. Did I do something wrong?
- The Factor Theorem A Polynomial P(x) has a factor x-a if an only if P(a) = 0 (x-a is a factor of P(x) if and only if P(a) = 0)
- At Nomial's house
- I guess when it comes to Chinese food there are always remainders.