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$ 3.2 Find the quotient and remainder using synthetic division method. (2x²-5x²-x+3) divide (x+3)
(2x³-5x²-8x+15) divide (x-3)
(x²+ x+5) divide (x-3)​

Sagot :

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✏️POLYNOMIAL

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Direction: Find the quotient and remainder using synthetic division method.

  • (2x² - 5x² - x + 3) ÷ (x + 3)

  • (2x³ - 5x² - 8x + 15) ÷ (x - 3)

  • (x² + x + 5) ÷ (x - 3)

Solution:

1.

[tex] \Large \begin{array}{c|rrrr}\text-3&2& \text - 5& \text - 1&3\\&& \text - 6& 33& \text - 96\\\hline& \blue2& \blue{\text - 11}& \blue{32}& \green{\text - 93}\end{array}[/tex]

- Therefore, the quotient is x² - 11x + 32 and the remainder is -93.

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2.

[tex] \Large \begin{array}{c|rrrr}3&2& \text - 5& \text - 8&15\\&&6&3& \text -15\\\hline& \blue2& \blue{1}& \blue{ \text - 5}& \green{0}\end{array}[/tex]

- Therefore, the quotient is x² + x - 5 and no remainder.

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3.

[tex]\Large \begin{array}{c|rrr}3&1&1&5 \\&&3&12& \\\hline& \blue1& \blue{4}& \green{17}&\end{array}[/tex]

- Therefore, the quotient is x + 4 and the remainder is 17

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