SOLUTION: When 4x raised to 2 -3𝑥−8 is divided by 𝑥-𝑎, the remainder is 2. Find the value of a

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Question 1170349: When 4x raised to 2 -3𝑥−8 is divided by 𝑥-𝑎, the remainder is 2. Find the value of a

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

When 4x%5E2+-3x-8 is divided by x-a, the remainder is 2. Find the value of a


......4x-3%2B4a
x-a|4x%5E2+-3x-8
......4x%5E2-4ax
.............-3x%2B4ax
.............-3x%2B3a+
.................4ax-3a
.................4ax-4a%5E2-8
...................-3a+%2B4a%5E2-8.................rearange
.................. ..4a%5E2+-3a-8 -> reminder

given that the remainder is 2
4a%5E2+-3a-8=2
4a%5E2+-3a-8-2=0
4a%5E2+-3a-10=0
a=%28-%28-3%29%2B-sqrt%28%28-3%29%5E2-4%2A4%28-10%29%29%29%2F%282%2A4%29
a=%283%2B-sqrt%289%2B160%29%29%2F8
a=%283%2B-sqrt%28169%29%29%2F8
a=%283%2B-13%29%2F8
solutions:
a=16%2F8=>a=2
or
a=-10%2F8=>a=-5%2F4