1. Find the quotient and remainder.
a) (x4 + 6x3 +13x2 + 15x - 1) /(x2 + 3x + 2)
Please answer the question
Answers
Answer:
Step-by-step explanation:
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]
★ 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!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 = 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!
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Answer:
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 !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 = 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
Step-by-step explanation: