# Find the Quotient and the Remainder When : 3x4 + 6x3 − 6x2 + 2x − 7 is Divided by X − 3. Verify Your Answer. - Mathematics

Sum

Find the quotient and the remainder when :
3x4 + 6x3 − 6x2 + 2x − 7 is divided by x − 3. verify your answer.

#### 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

Concept: Division of Algebraic Expressions - Dividing a Polynomial by a Polynomial
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 11 Algebraic Expressions
Exercise 11 (D) | Q 2.2 | Page 146