Question

Fill in each blank so that the resulting statement is trueFor the last box let’s put the quotient

Answer 1

`4x^2\text{ + }(19)/(3)x\text{ + 11 + }\frac{26}{3x\text{ - 3}}`Step-by-step explanation:
`\frac{12x^3+7x^2+14x\text{ }-7}{3x\text{ - 3}}`

To fill in the blank, we need to do the long division:

Since the division involves fraction, we will be dividing the numerator and denominator by 3 so it makes it easy to divide:

`\begin{gathered} \frac{12x^3+7x^2+14x\text{ }-7}{3x\text{ - 3}}=\text{ }12x^3+7x^2+14x\text{ }-7/3x\text{ - 3} \\ \frac{12x^3+7x^2+14x\text{ }-7}{3}\text{ }/(\frac{3x\text{ - 3}}{3}) \\ (12)/(3)x^3+(7)/(3)x^2+(14)/(3)x\text{ }-(7)/(3)/((3x)/(3)(-3)/(3)) \\ =\text{ 4}x^3+(7)/(3)x^2+(14)/(3)x\text{ }-(7)/(3)/(x-1) \\ =\text{ }\frac{\text{4}x^3+(7)/(3)x^2+(14)/(3)x\text{ }-(7)/(3)}{x\text{ - 1}} \end{gathered}`
`\begin{gathered} \frac{12x^3+7x^2+14x\text{ }-7}{3x\text{ - 3}}=4x^2\text{ + }(19)/(3)x\text{ + 11 + }\frac{(26)/(3)}{x\text{ - 1}} \\ \frac{(26)/(3)}{x\text{ - 1}}\text{ = }(26)/(3)/\text{ }(x-1)\text{ = }(26)/(3)*\text{ }(1)/(x-1) \\ \frac{(26)/(3)}{x\text{ - 1}}\text{ =}\frac{26}{3(x\text{ - 1) }}\text{ = }\frac{26}{3x\text{ - 3}} \\ \\ T\text{he result:} \\ \frac{12x^3+7x^2+14x\text{ }-7}{3x\text{ - 3}}=4x^2\text{ + }(19)/(3)x\text{ + 11 + }\frac{26}{3x\text{ - 3}} \end{gathered}`

completing the statement:

`\begin{gathered} \text{Begin the process by dividing }12x^3+7x^2+14x\text{ }-7\text{ by }3x\text{ - 3}, \\ which\text{ obtains }4x^2\text{ + }(19)/(3)x\text{ + 11 + }\frac{26}{3x\text{ - 3}}\text{. } \\ \text{Write this result above the quotient in the dividend} \\ \\ \text{obtains }4x^2\text{ + }(19)/(3)x\text{ + 11 as quotient and }26\text{ as remainder} \\ \end{gathered}`