Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\left. \begin{array} { l } { ( x - 3 ) ( x ^ { 3 } - 19 x + 30 ) } \\ { \frac { x ^ { 3 } - 19 x + 30 } { x - 3 } } \end{array} \right.$$

Answer

Gi*v*e*nHa*t*(x-3)*IM*s*a*f*a*c*t*o*r*o*f*(x-3)*(x+5)*(x-2);((x-3)*(x+5)*(x-2))/(x-3)

Solution


Factor \({x}^{3}-19x+30\) using Polynomial Division.
\[x^2\]\[2x\]\[-15\]
\[x-2\]\[x^3\]\[\]\[-19x\]\[30\]
\[x^3\]\[-2x^2\]
\[2x^2\]\[-19x\]\[30\]
\[2x^2\]\[-4x\]
\[-15x\]\[30\]
\[-15x\]\[30\]
\[\]
Rewrite the expression using the above.
\[{x}^{2}+2x-15\]
\[\begin{aligned}&GivenHat(x-3)\imath safactorof({x}^{2}+2x-15)(x-2)\\&\frac{({x}^{2}+2x-15)(x-2)}{x-3}\end{aligned}\]
Factor \({x}^{2}+2x-15\).
\[\begin{aligned}&GivenHat(x-3)\imath safactorof(x-3)(x+5)(x-2)\\&\frac{(x-3)(x+5)(x-2)}{x-3}\end{aligned}\]
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