Find undetermined coefficients in polynomial quotient and remainder

Reagan Gomez

Reagan Gomez

Answered question

2022-04-06

Find undetermined coefficients in polynomial quotient and remainder
P(x)=x46x3+16x225x+10

Answer & Explanation

Ouhamiptkg

Ouhamiptkg

Beginner2022-04-07Added 18 answers

Multiplying is easier than dividing, so we let the quotient have undetermined coef's and multiply.
Suppose rm x46x3+16x2!25x+10,=,(x2+cx+b),(x2!2x+k),+,x+a
Comparing coef's
x3  coef c2=6c=4
x2  coef b+8+k,=,16      b + k,=,8
x1  coef  2b!!4k=26b2k,=13
Adding the prior two equations yields k=5, so k=5, so b=8k=3, so a=

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