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# Synthetically Divide: (2x^3+x^2-22x+20)/(2x-3)

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3 months ago
 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:$$\displaystyle = \frac{2x^3+x^2-22x+22}{2x-3}$$ Read 119 times