[tex]f(x)=2x^3-11x^2+7x-5[/tex]
To find f(4) you divide the given polynomial into (x-4):
To divide:
1. Divide the first term of the dividend by the highest term of the divisor:
[tex]\frac{2x^3}{x}=2x^2[/tex]
2. Multiply the divisor by the result:
[tex]2x^2(x-4)=2x^3-8x^2[/tex]
3. Substract the product in step 2 from the appropiat terms of the dividend (when you substract the symbols change) (then bring down the next term from the dividend)
4. Repeat previous steps:
[tex]\frac{-3x^2}{x}=-3x[/tex][tex]-3x(x-4)=-3x^2+12x[/tex][tex]\frac{-5x}{x}=-5[/tex][tex]-5(x-4)=-5x+20[/tex]
As the remainder is -25:
[tex]f(4)=-25[/tex]
