Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Use the long division method to find the result when 3x³ + 11x² - 12x - 19 isdivided by 3x + 2. If there is a remainder, express the result in the formr(x)q(x) + b(z)

Sagot :

Given two polynomials f(x) and g(x), the division between them can be represented by:

[tex]\frac{f(x)}{g(x)}=q(x)+\frac{r(x)}{g(x)}[/tex]

Where q(x) is the quotient and r(x) is the remainder. From the problem, we identify:

[tex]\begin{gathered} f(x)=3x^3+11x^2-12x-19 \\ \\ g(x)=3x+2 \end{gathered}[/tex]

Then, using the long division method:

Finally:

[tex]\begin{gathered} r(x)=-7 \\ q(x)=x^2+3x-6 \end{gathered}[/tex]

And the result is:

[tex]\frac{f(x)}{g(x)}=x^2+3x-6-\frac{7}{3x+2}[/tex]

View image KennadieS284312
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.