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Question
Find the quotient and the remainder when 3x4 + 6x3 − 6x2 + 2x − 7 is divided by x − 3. in case, verify your answer.
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Solution
`"x"-3)overline(3"x"^4+6"x"^3-6"x"^2+2"x"-7)(3"x"^3+15"x"^2+39"x"+119`
3x4 − 9x3
− +
15x3 − 6x2 + 2x − 7
15x3 − 45x2
− +
39x2 + 2x − 7
39x2 − 117x
− +
119x − 7
119x − 357
− +
350
∴ Quotient = 3x3 + 15x2 + 39x + 119 and reminder = 350
Verification:
Dividend = Quotient × Divisor + Reminder
= (3x3 + 15x2 + 39x + 119) (x − 3) + 350
= 3x4 + 15x3 + 39x2 + 119x − 9x3 − 45x2 − 117x − 357 + 350
= 3x4 + 6x3 − 6x2 + 2x − 7 which is given
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