5 x ^ 3 - 13 x ^ 2 %2B 21 x - 14 \text by 3 - 2 x %2B x ^

1.	5 x ^ 3 - 13 x ^ 2 %2B 21 x - 14 \text by 3 - 2 x %2B x ^ 2
Answer» Given f(x) = 5x^3 - 13x^2 + 21x - 14. Given g(x) = 3 - 2x + x^2. We need to divide f(x) by g(x). 5x - 3 ---------------------------------= > x^2 - 2x + 3) 5x^3 - 13x^2 + 21x - 14 5x^3 - 10x^2 + 15x --------------------------------- -3x^2 + 6x - 14 - 3x^2 + 6x - 9 -------------------------------- -5. Here, Dividend = 5x^3 - 13x^2 + 21x - 14 Divisor = 3 - 2x + x^2 Quotient = 5x - 3 Remainder = -5 Division Algorithm: Dividend = Divisor * Quotient + Remainder = (3 - 2x + x^2) * (5x - 3) + (-5) = 15x - 9 - 10x^2 + 6x + 5x^3 - 3x^2 - 5 = 5x^3 - 13x^2 + 21x - 14. LHS = RHS Like my answer if you find it useful!

5 x ^ 3 - 13 x ^ 2 %2B 21 x - 14 \text by 3 - 2 x %2B x ^ 2

Answer»

Given f(x) = 5x^3 - 13x^2 + 21x - 14.

Given g(x) = 3 - 2x + x^2.

We need to divide f(x) by g(x).

5x - 3 ---------------------------------= > x^2 - 2x + 3) 5x^3 - 13x^2 + 21x - 14

5x^3 - 10x^2 + 15x ---------------------------------

-3x^2 + 6x - 14

- 3x^2 + 6x - 9 -------------------------------- -5.

Here,

Dividend = 5x^3 - 13x^2 + 21x - 14

Divisor = 3 - 2x + x^2

Quotient = 5x - 3

Remainder = -5

Division Algorithm:

Dividend = Divisor * Quotient + Remainder

= (3 - 2x + x^2) * (5x - 3) + (-5)

= 15x - 9 - 10x^2 + 6x + 5x^3 - 3x^2 - 5

= 5x^3 - 13x^2 + 21x - 14.

LHS = RHS

Like my answer if you find it useful!