Question

find the quotient and remainder using long division for: $\frac{x^{2}+7x + 15}{x + 3}$. the quotient is the remainder is question help: video 1 video 2 read 1 written example 1 message instructor submit question

Explanation:

Step1: Divide leading terms

Divide $x^{2}$ by $x$. We get $x$ since $\frac{x^{2}}{x}=x$.

Step2: Multiply and subtract

Multiply $x + 3$ by $x$ to get $x^{2}+3x$. Subtract $x^{2}+3x$ from $x^{2}+7x + 15$: $(x^{2}+7x + 15)-(x^{2}+3x)=4x + 15$.

Step3: Divide new leading term

Divide $4x$ by $x$, we get $4$ since $\frac{4x}{x}=4$.

Step4: Multiply and subtract again

Multiply $x + 3$ by $4$ to get $4x+12$. Subtract $4x + 12$ from $4x + 15$: $(4x + 15)-(4x+12)=3$.

Answer:

The quotient is $x + 4$
The remainder is $3$