How do you use synthetic division to divide $\frac{2 x^{3} - x^{2} + 5 x - 12}{2 x - 3}$ $(2x^3-x^2+5x-12) /(2x - 3)$ ?

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Answer 1 · 2018-03-28T11:46:28

Quotient is $x^{2} + x + 4$ $x^2+x+4$ and remainder is $0$ $0$ .

$2 x^{3} - x^{2} + 5 x - 12$ $2x^3-x^2+5x-12$

= $2 x^{3} - 3 x^{2} + 2 x^{2} - 3 x + 8 x - 12$ $2x^3-3x^2+2x^2-3x+8x-12$

= $x^{2} \cdot (2 x - 3) + x \cdot (2 x - 3) + 4 \cdot (2 x - 3)$ $x^2*(2x-3)+x*(2x-3)+4*(2x-3)$

= $(2 x - 3) \cdot (x^{2} + x + 4)$ $(2x-3)*(x^2+x+4)$

Hence quotient is $x^{2} + x + 4$ $x^2+x+4$ and remainder is $0$ $0$ .

How do you use synthetic division to divide 2x3−x2+5x−122x−3(2x^3-x^2+5x-12) /(2x - 3) ?