the quotient of $(x^{4}+5x^{3}-3x - 15)$ and $(x^{3}-3)$ is a polynomial. what is the quotient?\n$x^{7}+5x^{6…

the quotient of $(x^{4}+5x^{3}-3x - 15)$ and $(x^{3}-3)$ is a polynomial. what is the quotient?\n$x^{7}+5x^{6}-6x^{4}-30x^{3}+9x + 45$\n$x - 5$\n$x + 5$\n$x^{7}+5x^{6}+6x^{4}+30x^{3}+9x + 45$

the quotient of $(x^{4}+5x^{3}-3x - 15)$ and $(x^{3}-3)$ is a polynomial. what is the quotient?\n$x^{7}+5x^{6}-6x^{4}-30x^{3}+9x + 45$\n$x - 5$\n$x + 5$\n$x^{7}+5x^{6}+6x^{4}+30x^{3}+9x + 45$

Answer

Answer:

C. $x + 5$

Explanation:

Step1: Use polynomial long - division

We divide $x^{4}+5x^{3}-3x - 15$ by $x^{3}-3$. First, divide the leading term of the dividend $x^{4}+5x^{3}-3x - 15$ (which is $x^{4}$) by the leading term of the divisor $x^{3}-3$ (which is $x^{3}$). $\frac{x^{4}}{x^{3}}=x$.

Step2: Multiply and subtract

Multiply $x^{3}-3$ by $x$ to get $x^{4}-3x$. Subtract this from the dividend: $(x^{4}+5x^{3}-3x - 15)-(x^{4}-3x)=5x^{3}-15$.

Step3: Divide again

Divide the leading term of the new dividend $5x^{3}-15$ (which is $5x^{3}$) by the leading term of the divisor $x^{3}$ to get $5$.

Step4: Multiply and subtract again

Multiply $x^{3}-3$ by $5$ to get $5x^{3}-15$. Subtract this from $5x^{3}-15$: $(5x^{3}-15)-(5x^{3}-15)=0$. So the quotient is $x + 5$.