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C3 Remainder Theorem

Could somebody please explain the remainder theorem from C3 Chapter 1 to me please? :tongue:
As in I get that you have
F(x)=Q(x) x divisor + remainder
and I know how to work out what Q(x), but I'm not sure how you're supposed to know what the remainder is...any help would be appreciated :smile:
Reply 1
Avatar for Notnek
Notnek
21
Original post by 29Bilal96
Could somebody please explain the remainder theorem from C3 Chapter 1 to me please? :tongue:
As in I get that you have
F(x)=Q(x) x divisor + remainder
and I know how to work out what Q(x), but I'm not sure how you're supposed to know what the remainder is...any help would be appreciated :smile:

83=2+23\frac{8}{3} = 2 + \frac{2}{3}

⇒8=2×3+2\Rightarrow 8 = 2 \times 3 + 2


x3+2x+1=(x2−x+1)+1x+1\displaystyle \frac{x^3+2}{x+1} = (x^2-x+1) + \frac{1}{x+1}

⇒x3+2=(x2−x+1)(x+1)+1\displaystyle \Rightarrow x^3+2 = (x^2-x+1)(x+1) + 1


Can you see how the remainder theorem is linked to algebraic division that you did in C2?
Reply 2
Avatar for 29Bilal96
29Bilal96
OP
14
Oops dw, found the answer in another thread :tongue:
Reply 3
Avatar for 29Bilal96
29Bilal96
OP
14
Original post by notnek
83=2+23\frac{8}{3} = 2 + \frac{2}{3}

⇒8=2×3+2\Rightarrow 8 = 2 \times 3 + 2


x3+2x+1=(x2−x+1)+1x+1\displaystyle \frac{x^3+2}{x+1} = (x^2-x+1) + \frac{1}{x+1}

⇒x3+2=(x2−x+1)(x+1)+1\displaystyle \Rightarrow x^3+2 = (x^2-x+1)(x+1) + 1


Can you see how the remainder theorem is linked to algebraic division that you did in C2?


thanks i get it now, i was just unsure about what form the remainder should be, but i think it should always be order one less than the divisor

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