Question

Drag the tiles to the correct boxes to complete the pairs.13 – 7:2 + 13.1 - 3(1)Rewrite the rational expressionin the form 9() + (3), and then match g(x), rx), and b(x) to the correctexpressions

Answer 1

`(x^3-7x^2+13x-3)/(x-3)`

Use the long division method,

`\begin{gathered} x-3|\text{ }x^3-7x^2+13x-3\text{ }=\text{ }x^2 \\ \text{ }x^3-3x^2 \\ x-3|-4x^2+13x-3\text{ = -4}x \\ \text{ }-4x^2+12x-3 \\ x-3|\text{ }x-3\text{ = 1} \\ \text{ 0} \end{gathered}`

Therefore,

`(x^3-7x^2+13x-3)/(x-3)=x^2-4x+1\text{ +}(0)/(x-3)`

Hence,

`\begin{gathered} q(x)\text{ = }x^2-4x+1\text{ } \\ b(x)\text{ = }x-3 \\ r(x)\text{ = 0} \end{gathered}`