IB DP Maths: AA HL复习笔记2.7.1 Factor & Remainder Theorem
What is the factor theorem?
- The factor theorem is used to find the linear factors of polynomial equations
- This topic is closely tied to finding the zeros and roots of a polynomial function/equation
- As a rule of thumb a zero refers to the polynomial function and a root refers to a polynomial equation
- For any polynomial function P(x)
- (x - k) is a factor of P(x) if P(k) = 0
- P(k) = 0 if (x - k) is a factor of P(x)
How do I use the factor theorem?
Exam Tip
- A common mistake in exams is using the incorrect sign for either the root or the factor
- If you are asked to find integer solutions to a polynomial then you only need to consider factors of the constant term
Worked Example
Remainder Theorem
What is the remainder theorem?
- The remainder theorem is used to find the remainder when we divide a polynomial function by a linear function
- When any polynomial P(x) is divided by any linear function (x - k) the value of the remainder R is given by P(k) = R
- Note, when P(k) = 0 then (x - k) is a factor of P(x)
How do I use the remainder theorem?
- Consider the polynomial function P(x) = anxn+ an-1xn-1 + … + a1x + a0 and the linear function (x - k)
- Then, due to the remainder theorem P(k) = ankn+ an-1kn-1 + … + a1k + a0 = R
Worked Example
转载自savemyexams
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