SOLUTION: Express f(x) in the form f(x)=(x-k)q(x)+r for the given value of k. f(x)=3x^4-2x^3-15x^2-x;k=4 f(x)=(x-___)(___)+_____

Algebra ->  Expressions-with-variables -> SOLUTION: Express f(x) in the form f(x)=(x-k)q(x)+r for the given value of k. f(x)=3x^4-2x^3-15x^2-x;k=4 f(x)=(x-___)(___)+_____      Log On


   



Question 925497: Express f(x) in the form f(x)=(x-k)q(x)+r for the given value of k.
f(x)=3x^4-2x^3-15x^2-x;k=4
f(x)=(x-___)(___)+_____

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Express f%28x%29 in the form f%28x%29=%28x-k%29q%28x%29%2Br for the given value k:

f%28x%29=3x%5E4-2x%5E3-15x%5E2-x; k=4
f%28x%29=%28x-___%29%28___%29%2B_____

write down coefficients:
3)3...-2...-15...-1... 0 -> multiply by k=4
. ___12___40__100__396___add
. 3. .10.... . 25.....+99.....+396 <== remainder "r"
coefficients for q%28x%29
3. .10. .... 25..... 99.... 396 means
q%28x%29+=+3x%5E3+%2B+10x%5E2+%2B+25x+%2B+99
f%28x%29+=+%28x+-+4%29%283x%5E3+%2B+10x%5E2+%2B+25x+%2B+99%29+%2B+396 <==ANSWER