Question

What are the quotient and remainder of (3x^4-2x^3+7x-4)/(x-3)

Answer 1

Answer: Remainder: 206

Quotient: 3x³+7x²+21x+70 + $\frac{206}{x-6}$

Step-by-step explanation: You can either use long division or synthetic division. I will use synthetic division: 3 | 3 -2 0 7 -4... the remainder is 206 and the quotient is 3x³+7x²+21x+70  + 206/x-6

Answer 2

The remainder is 206 and the quotient is ($3x^{4} - 2x^{3} + 7x -4$ -206) /(x - 3)

What is quotient in a division?

A result obtained by dividing one quantity by another is called a quotient.

What is remainder in a division?

Remainder is the value left after the division.

How to find the quotient and remainder of the division?

• We know that, if (x - h) divides a function f(x) then f(h) is the remainder.

∴ Here the remainder will be putting x = 3 in the dividend.

So, remainder = $3(3)^{4} - 2(3)^{3} + 7(3) - 4$ = 206

• We can get the quotient by the quotient remainder rule which says

in a division, dividend is equal to divisor multiplied by quotient plus remainder.

Let the quotient be Q(x)

Here,  we can write,

$3x^{4} - 2x^{3} + 7x -4$  = (x - 3)Q(x) + 206

⇒ Q(x) = ($3x^{4} - 2x^{3} + 7x -4$ -206) / (x - 3)

So, the required quotient is  ($3x^{4} - 2x^{3} + 7x -4$ -206) / (x - 3)

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