# C2-The Factor Theorem and The Remainder Theorem

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- Created by: evie
- Created on: 15-05-13 14:37

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**You can factorise polynomials by using the factor theorem:** **If f(x) is a polynomial, and f(p)=0, then (x-p) is a factor.**

** ** Examples:

1) Show that (x-2) is a factor of x³+x²-4x-4 by using the factor theorem.

f(2)=2³+2²-(4×2)-4 f(2)=8+4-8-4 f(2)=0

There is no remainder, therefore it is a factor.

2)Factorise 2x³+x²-18x-9

- we write the polynomial as a function, and try different values of x until we get the answer to be 0. (although it’s not on the spec, the value of x will always be a factor of the last number, in this case, -9)

So the values of x will be -1, 1, -3, 3, -9, or 9

f(1)=2×(1³)+1²-(18×1)-9 f(1)=-24 ~-1…

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