Question

Find the quotient and remainder.
a) (x⁴+ 6x³ +13x² + 15x - 1) ÷ (x² + 3x + 2)​

Answer 1

Answer:

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]

Verification :

★ Dividend Remainder = Divisor Quotient +

x² + 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 = x² + 3x³+4x²+ 3x³ + 9x² + 12x + 3x - 1

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

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

15x - 1

Hence, Verified!

Answer 2

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