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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.
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