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Identities, factor structure and coefficients
Free examples and worked answers. No account needed.
Practise the method.
Identities, factor structure and coefficients
Optional extension. Identities, factor structure and coefficients
Example 1
Find the coefficient of x2 in (x+3)(x−2)(x+4).
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Answer: 5
- An x2 term uses the constant from exactly one bracket.
- Add 3,−2 and 4:5.
Example 2
P(x)=x3+kx+2. When P(x) is divided by x−3, the remainder is 41. Find k.
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Answer: 4
- The remainder theorem gives P(3)=41.
- Hence 27+3k+2=41
- k=4.
Example 3
Find the coefficient of x2 in (x+6)(x−3)(x+2).
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Answer: 5
- An x2 term uses the constant from exactly one bracket.
- Add 6,−3 and 2:5.
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