The polynomial - 3x^3 + 2x^2 + 5x - 1, when divided by 2x + 1, leaves a remainder equal to
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Answer:Let the remainder be R1 and R2 as given :
R1 = ax^3 + 3x^2 - 3
Now, x - 4 => x = 4
R1 = a(4)^3 + 3(4)^2 - 3
R1 = 64a + 48 - 3
R1 = 64a + 45
R2 = 2x^2 - 5x + a
R2 = 2(4)^2 - 5(4) + a
R2 = 32 - 20 + a
R2 = 12 + a
R1 + R2 = 0
64a + 45 + 12 + a = 0
65a = - 57
a = - 57/65
2R1 - R2 = 0
2( 64a + 45 ) - 12 - a = 0
128a + 90 - 12 - a = 0
127a = - 78
a = - 78/127
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But friend, same question I have also done but there is a slight difference in question. In my book there is 2x^3 - 5x + a instead of 2x^2 - 5x + a. So, I am giving pic of that too.