Determine c if x-2 is a factor of x^3-5x^2+cx-2.
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Nov 7, 2005 #3 Hello, anniem! Are you familiar with the Remainder Theorem? \(\displaystyle f(x)\) is divisible by \(\displaystyle (x\,-\,a)\) if and only if \(\displaystyle f(a)\,=\,0\) Determine \(\displaystyle c\) if \(\displaystyle x-2\) is a factor of \(\displaystyle f(x)\:=\:x^3\,-\,5x^2\,+\,cx\,-\,2\) Click to expand... The Theorem says: if \(\displaystyle (x-2)\) is a factor of \(\displaystyle f(x)\), then \(\displaystyle f(2)\,=\,0\) We have: .\(\displaystyle f(2)\:=\:2^3\,-\,5\cdot2^2\,+\,c\cdot2\,-\,2\:=\:0\;\;\Rightarrow\;\;c\,=\,7\)
Hello, anniem! Are you familiar with the Remainder Theorem? \(\displaystyle f(x)\) is divisible by \(\displaystyle (x\,-\,a)\) if and only if \(\displaystyle f(a)\,=\,0\) Determine \(\displaystyle c\) if \(\displaystyle x-2\) is a factor of \(\displaystyle f(x)\:=\:x^3\,-\,5x^2\,+\,cx\,-\,2\) Click to expand... The Theorem says: if \(\displaystyle (x-2)\) is a factor of \(\displaystyle f(x)\), then \(\displaystyle f(2)\,=\,0\) We have: .\(\displaystyle f(2)\:=\:2^3\,-\,5\cdot2^2\,+\,c\cdot2\,-\,2\:=\:0\;\;\Rightarrow\;\;c\,=\,7\)
