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LONG ANSWER TYPE QUESTION With out actual division, prove that a + 2a³ - 2a + 2a - 3 is exactly divisible a² + 2a - 3.​

LONG ANSWER TYPE QUESTION With out actual division, prove that a + 2a³ - 2a + 2a - 3 is exactly divisible a² + 2a - 3.​
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LONG ANSWER TYPE QUESTION With out actual division, prove that a + 2a³ - 2a + 2a - 3 is exactly divisible a² + 2a - 3.​

asked
User Snea
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1 Answer

4 votes

Answer:

Hi,

Explanation:


a^2+2a-3=a^2-a+3a-3=a(a-1)+3(a-1)=(a-1)(a+3)\\Let's\ say\ P(a)=a^4+2a^3-2a^2+2a-3\\\\P(1)=1+2-2+2-3=0\\\\P(-3)= (-3)^4+2*(-3)^3-2*(-3)^2+2*(-3)-3\\=81-54-18-6-3\\=0\\

P(a) is exactly divisible by (a-1)(a+3) thus by a²+2a-3

answered
User Hasteq
by
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