Question

Hi. I need help with these questions.
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Answer 1

Explanation:

Given

• P(x) = 6x³ + 4x² - x + 5

Divide by the following:

(a) 3x² + 2x + 1

• 6x³ + 4x² - x + 5 =
• 2x(3x²) + 2x(2x) + 2x - 3x + 5 =
• 2x(3x² + 2x + 1) + (-3x + 5)

Quotient = 2x, remainder = -3x + 5

(b) x³ - 3x + 2

• 6x³ + 4x² - x + 5 =
• 6(x³) - 6(3x) + 6(2) + 4x² + 22x - 7
• 6( x³ - 3x + 2) + (4x² + 22x - 7)

Quotient = 6, remainder = 4x² + 22x - 7

(c) 6x² + x - 2

• 6x³ + 4x² - x + 5 =
• x(6x²) + x(x) - x(2) + 3x² + x + 5 =
• x(6x² + x - 2) + (3x² + x + 5)

Quotient = x, remainder = 3x² + x + 5