Given that $n\,$ is a positive integer, use your result from part (b) to determine whether $10n^3 + 9n^2 + 10n + 4$ can ever be a prime number. Justify your answer.

[3]

1.2.10 Manipulating polynomials Questions

A Level
Maths
1.2.10 Manipulating polynomials

A Level
Maths OCR
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1.2.10 Manipulating polynomials

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Question 41

The mechanical stress $S\,$ measured in a reinforced composite beam depends on a reinforcement parameter $k\,$ and is modeled by the function:

S(k) = 10k^3 + 9k^2 + 10k + 4

Use the factor theorem to show that $(2 k + 1)$ is a factor of $S (k)$ .

[3]

Express $S (k)$ in the form

S(k) = (2k + 1)(ak^2 + bk + c)

where $a$ , $b\,$ and $c\,$ are integers to be determined.

[4]

Given that $n\,$ is a positive integer, use your result from part (b) to determine whether $10n^3 + 9n^2 + 10n + 4$ can ever be a prime number. Justify your answer.

[3]

1.2.10 Manipulating polynomials Questions

A Level
Maths
1.2.10 Manipulating polynomials