Use the long division method to find the result when 2x3 - 9x2 - x + 30 is divided by x - 3 .

Mathematics

1 answer:

meriva3 years ago

4 0

Answer:

F(x) = 2x3 - 9x2 - x + 30

Step-by-step explanation:

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$\dfrac{ \dfrac{x+3}{4x^2-16} }{ \dfrac{2x^2+10x+12}{2x-4} }$

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Write the divide fraction horizontally:
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$= \dfrac{x+3}{4x^2-16} \div \dfrac{2x^2+10x+12}{2x-4}$

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Factorise the numerators and denominators when possible:
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$= \dfrac{x+3}{4(x+2)(x-2)} \div \dfrac{ 2(x + 3) (x + 2)}{2(x-2)}$

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Convert the divide fraction to multiplication fraction
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$= \dfrac{x+3}{4(x+2)(x-2)} \times \dfrac{2(x-2)}{2(x+3)(x+2)}$

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Cancel the factors
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$= \dfrac{1}{4(x+2)} \times \dfrac{1}{(x+2)}$

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Combine to single fraction
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$= \dfrac{1}{4(x+2)^2}$

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Step-by-step explanation:

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Use the long division method to find the result when 2x3 - 9x2 - x + 30 is divided by x - 3 .​

Use the long division method to find the result when 2x3 - 9x2 - x + 30 is divided by x - 3 .