Math, asked by sunil9161, 1 year ago

Find the value of k for which a-3b is factor ofa4-7a²b²+kb4. Hence ,for the value of k, factorise a4-7a²b²+kb4 completeky.

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Answered by manpreetsingh23

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Answered by jashankaler143

Divide by long division, inserting zero terms for missing terms +0a³b and +0ab³: a³ +3a²b +2ab²+ 6b³ a-3b)a⁴+0a³b-7a²b²+0ab³+ kb⁴ a⁴-3a³b 3a³b-7a²b² 3a³b-9a²b² 2a²b²+0ab³ 2a²b²-6ab³ 6ab³+ kb⁴ 6ab³-18b⁴ kb⁴+18b⁴ <-- remainder The remainder must = 0 so that a-3b will be a factor of a⁴-7a²b²+kb⁴. kb⁴+18b⁴ = 0 (k+18)b⁴ = 0 k+18=0; b⁴=0 k=-18; b=0 There is a trivial case for b=0 and k is any number, which we ignore. So k = -18 a⁴-7a²b²-18b⁴ (a²+2b²)(a²-9b²) (a²+2b²)(a-3b)(a+3b)
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