Question

Find the quotient and remainder of (x^4+6x^3+13x^2+15x-1)/x^2+3x+2

Answer 1

$\sf \: Solution :$

p(x) = x⁴ + 6x³ + 13x² + 15x - 1

g(x) = x² + 3x + 2

By Long Division Method, we obtained :

• Quotient - x² + 3x + 4

• Remainder = 3x - 1

[Refer to the attachment]

$\sf \: Verification :$

★ Dividend = Divisor × Quotient + Remainder

→ x⁴ + 6x³ + 13x² + 15x - 1 = (x² + 3x + 2) (x² + 3x + 4) + 3x - 1

→ x⁴ + 6x³ + 13x² + 15x - 1 = x²(x² + 3x + 4) + 3x(x² + 3x + 4) + 2(x² + 3x + 4) + 3x - 1

→ x⁴ + 6x³ + 13x² + 15x - 1 = x⁴ + 3x³ + 4x² + 3x³ + 9x² + 12x + 3x - 1

→ x⁴ + 6x³ + 13x² + 15x - 1 = x⁴ + 3x³ + 3x³ + 4x² + 9x² + 12x + 3x - 1

→ x⁴ + 6x³ + 13x² + 15x - 1 = x⁴ + 6x³ + 13x² + 15x - 1

Hence, Verified!

Answer 2

Step-by-step explanation:

Remainder --- 3x-1

Quotient ---- x²+ 3x +4

We have solved by long division method