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Polynomials

Short Answer Type

231. Factorise: $straight x squared plus 3 square root of 3 straight x end root plus 6$

Solution not provided.

Ans. $open parentheses straight x plus square root of 3 close parentheses space left parenthesis x plus 2 square root of 3 right parenthesis$

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232. Factorise: x⁴ + 4x² + 3

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233. Factorise: x⁶ - y⁶

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234. Factorise: 4a² - 9b² - 2a - 3b

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235. Find the value of x³ + y³ - 12xy + 64, when x + y = -4.

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236. Without finding the cubes, factorise and find the value of:

open parentheses 1 fourth close parentheses cubed plus open parentheses 1 third close parentheses cubed minus open parentheses 7 over 12 close parentheses cubed

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237. If x + y + z = 1, xy + yz + zx = -1 and xyz = -1, find the value of x³ + y³ + z³.

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238. Factorise: a¹²y⁴ - a⁴y¹².

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239. If a + b = 10 and a² + b² = 58, find the value of a³ + b³.

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240. Factorise: 27a³ + 8b³ + 54a²b + 36ab².

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