Question

1. $(x^{3}-14x + 15)div(x - 3)$

Explanation:

Step1: Rewrite dividend with $x^2$ term

$x^3 + 0x^2 -14x +15$

Step2: Divide $x^3$ by $x$

$\frac{x^3}{x}=x^2$

Step3: Multiply divisor by $x^2$

$x^2(x-3)=x^3-3x^2$

Step4: Subtract from dividend

$(x^3+0x^2-14x+15)-(x^3-3x^2)=3x^2-14x+15$

Step5: Divide $3x^2$ by $x$

$\frac{3x^2}{x}=3x$

Step6: Multiply divisor by $3x$

$3x(x-3)=3x^2-9x$

Step7: Subtract from new dividend

$(3x^2-14x+15)-(3x^2-9x)=-5x+15$

Step8: Divide $-5x$ by $x$

$\frac{-5x}{x}=-5$

Step9: Multiply divisor by $-5$

$-5(x-3)=-5x+15$

Step10: Subtract to find remainder

$(-5x+15)-(-5x+15)=0$

Answer:

$x^2 + 3x - 5$