smc-4242-40-Long division

Polynomials, SMB-012

Show (1 mark)

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Express in the form where is a quadratic factor. (2 marks)

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Justify that only has one zero. (2 marks)

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ii.

iii.

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i. .

ii.

iii.

Let .

Show that . (1 mark)

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Hence, factor the polynomial as , where is a quadratic polynomial. (2 marks)

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ii.

Consider the polynomial .

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ii.

Let .

Show that . (1 mark)

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Hence, factor the polynomial as , where is a quadratic polynomial. (2 marks)

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i.

ii.

Consider the polynomials and .

Given that is divisible by , show that . (1 mark)

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Find all the zeros of when . (2 marks)

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i.

ii.