Question

Julie divided x^4 + 3x^3 -9x^2 +6 by a polynomial. Her answer was x^3 - 2x^2 + x - 5 with a remainder of 31. What polynomial did Julie divide by?

Answer 1

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Answer 2

How would I find the divisor? Would I use the equation Dividend - Remainder / Quotient ?

Answer 3

let the polynomial be ax+b then
x^4 +3x^3-9x^2+6=(ax+b)(x^3-2x^2+x-5)+31
solve R.H.S and equate the terms with like powers.

Answer 4

Do I expand (ax + b ) with (x^3-2x^2+x-5) ?

Answer 5

yes

Answer 6

I get ax^4 + 2ax^3 + ax ^2 -5 ax + bx^3 - 2bx^2 +bx - 5b + 3. What do I do now?

Answer 7

ax^4+(2a+b)x^3+(...........)x^2+(......)x+3+31=x^4+3x^3-9x^2+(.....)x+6
equate the terms with like powers and then find a and b.

Answer 8

Thank you so much!