The remainder is [tex]\dfrac{2}{5}[/tex].
Important information:
- [tex](3x - 2)[/tex] is divided by [tex](5x - 4)[/tex].
Remainder theorem:
According to the remainder theorem, if a polynomial [tex]p(x)[/tex] is divided by [tex](x-c)[/tex] then the remainder is [tex]p(c)[/tex].
The dividend is [tex]p(x)=(3x - 2)[/tex] and the divisor is [tex](5x - 4)[/tex].
[tex](5x - 4)=0[/tex]
[tex]x=\dfrac{4}{5}[/tex]
Using the remainder theorem, the remainder is [tex]p\left(\dfrac{4}{5}\right)[/tex].
[tex]p\left(\dfrac{4}{5}\right)=3\left(\dfrac{4}{5}\right)-2[/tex]
[tex]p\left(\dfrac{4}{5}\right)=\dfrac{12}{5}-2[/tex]
[tex]p\left(\dfrac{4}{5}\right)=\dfrac{12-10}{5}[/tex]
[tex]p\left(\dfrac{4}{5}\right)=\dfrac{2}{5}[/tex]
Therefore, the remainder is [tex]\dfrac{2}{5}[/tex].
Find out more about 'Remainder theorem' here:
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