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Synthetically Divide: (2x^3+x^2-22x+20)/(2x-3)
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Synthetically Divide: (2x^3+x^2-22x+20)/(2x-3)
Divide by synthetic division: \((2x^3+x^2-22x+20)\div (2x-3)\)
Begin by solving for \(x\) in the
divisor
:
\(2x-3=0\)
\(\displaystyle x=\frac{3}{2}\)
Now perform synthetic division:
Given a remainder of \(4\), write the expression as:
\(\displaystyle 2x^2+4x-16-\frac{4}{x-\frac{3}{2}}\)
Recall that you set the divisor \(2x-3\) equal to \(0\) at the start. Since \(x\) has a coefficient of \(2\), divide the expression above by \(2\) as well.
\(\displaystyle \frac{\left(2x^2+4x-16-\frac{4}{x-\frac{3}{2}}\right)}{2}\)
Simplify by finding a common denominator in the numerator:
\(\displaystyle =\frac{\frac{\left(2x^2+4x-16\right)\left(x-\frac{3}{2}\right)-4}{x-\frac{3}{2}}}{2}\)
\(\displaystyle =\frac{\left(2x^2+4x-16\right)\left(x-\frac{3}{2}\right)-4}{x-\frac{3}{2}}\div 2\)
\(\displaystyle =\frac{\left(2x^2+4x-16\right)\left(x-\frac{3}{2}\right)-4}{x-\frac{3}{2}}\times \frac{1}{2}\)
Expand and multiply:
\(\displaystyle = \frac{2x^3+x^2-22x+22}{2x-3} \)
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Synthetically Divide: (2x^3+x^2-22x+20)/(2x-3)
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