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311. Find the value of ‘a’ if (x - a) is a factor of x⁵ - a²x³ + 2x + a + 3, hence factorise x²- 2ar -3.

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312. If x - 2y = 11 and xy = 8, find the value of x³ - 8y³.

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313. If x + 2y = 8 and xy = 6, find the value of x³ + 8y³.

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314.

If $straight x plus 1 over straight x equals 3 comma$ then the value $straight x squared plus 1 over straight x squared$ .

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315. Factorise: (x² - 2x)² - 11 (x² - 2x) + 24

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316.

If $straight x plus 1 over straight x equals 5 comma$ then the value $straight x to the power of 6 plus 1 over straight x to the power of 6$ .

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317.

Prove that 2x³ + 2y³ + 2z³ - 6xyz
= (x + y + z) [(x - y)² + (y - z)² + (z - x)²].

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318.

If x² - 3x + 2 is a factor of x⁴ - ax² + b, then find a and b.

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319.

The volume of a cube is given by the polynomial
p(x) = 8x³ - 36x² + 54x - 27

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Solution not provided.

Ans. (x - 1) (x + 1) (x - 4) (x + 2)

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