What is factor theorm and what is reminder theorm plzzz explain
Answers
Remainder Theorem. ... If you divide a polynomial f(x) by (x - h), then the remainder is f(h). The theorem states that our remainder equals f(h). Therefore, we do not need to use long division, but just need to evaluate the polynomial when x = h to find the remainder.
What if we calculate f(c) and it is 0?
... that means the remainder is 0, and ...
... (x−c) must be a factor of the polynomial!
We see this when dividing whole numbers. For example 60 ÷ 20 = 3 with no remainder. So 20 must be a factor of 60.
Example: x2−3x−4
f(4) = (4)2−3(4)−4 = 16−12−4 = 0
so (x−4) must be a factor of x2−3x−4
And so we have:
The Factor Theorem:
When f(c)=0 then x−c is a factor of f(x)
And the other way around, too:
When x−c is a factor of f(x) then f(c)=0
Answer:
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