Question

Divide 6x cube + 2x square - 4x + 3 by 3x square - 2x + 1

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• p(x) = 6x³ + 2x² - 4x + 3

• g(x) = 3x² - 2x + 1

From Long Division Method, we obtained :

• Quotient = 2x + 2

• Remainder = - 2x + 1

Verification :

★ Dividend = Divisor × Quotient + Remainder

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

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

→ 6x³ + 2x² - 4x + 3 = 6x³ - 4x² + 2x + 6x² - 4x + 2 - 2x + 1

→ 6x³ + 2x² - 4x + 3 = 6x³ - 4x² + 6x² + 2x - 4x - 2x + 2 + 1

→ 6x³ + 2x² - 4x + 3 = 6x³ + 2x² - 4x + 3

$\dag \sf \: Hence, \: Proved! \:$