Title: Synthetically Divide: (2x^3+x^2-22x+20)/(2x-3) Post by: bio_man on Jan 26, 2022 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: (https://biology-forums.com/gallery/44/6_26_01_22_1_52_17.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=44203) 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: \(\displaystyle = \frac{2x^3+x^2-22x+22}{2x-3} \) |