Year 11 · Specialist Mathematics

Real Polynomials

Free examples and worked answers. No account needed.

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Practise the method.

Remainder and factor theorems for real polynomials.

Example 1

Polynomial curve with a movable input probe and a fixed division input.xy0division at x = 2P(x): same polynomial as the question
Move the input probe and connect the marked input with the remainder theorem.
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Answer:

Example 2

Polynomial curve with an illustrative vertical shift and the given root marked on the x-axis.xy0given root x = 4Unknown k shifts the whole curve vertically
Move the illustrative curve vertically towards the fixed root. The slider explores shifts, not numerical values of k.
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Answer:

Example 3

Polynomial curve with a movable input probe and a fixed division input.xy0division at x = 1P(x): same polynomial as the question
Move the input probe and connect the marked input with the remainder theorem.
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Answer: