Given:
The dividend is,
[tex]x^2+5x-24[/tex]The divisor is,
[tex]x-6[/tex]To find: The remainder
Explanation:
Let us take,
[tex]p(x)=x^2+5x-24[/tex]Using the remainder theorem,
Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number.
If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).
Here,
[tex]a=6[/tex]Substitute the value of a in the above polynomial.
[tex]\begin{gathered} p(6)=6^2+5(6)-24_{} \\ =36+30-24 \\ =42 \end{gathered}[/tex]Hence, the remainder is 42.
Final answer: The remainder is 42.
