Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Your answer should be in the form $p(x)+\frac{k}{x-1}$ where $p$ is a polynomial and $k$ is an integer. $\frac{x^2+6x-4}{x-1}$

View step-by-step help

View step-by-step help

Simplify exponential expressions using exponent rules

Full solution

Q. Your answer should be in the form

p(x)+\frac{k}{x-1}

where

p

is a polynomial and

k

is an integer.

\frac{x^2+6x-4}{x-1}

Perform Polynomial Long Division: Step $1$ : Perform polynomial long division on $(x^2 + 6x - 4)$ by $(x - 1)$ . Divide the leading term of the numerator by the leading term of the denominator: $x^2 / x = x$ . Multiply $x$ by $(x - 1)$ to get $x^2 - x$ . Subtract $(x^2 - x)$ from $(x^2 + 6x - 4)$ to get $7x - 4$ .
Continue Division Process: Step $2$ : Continue the division process. $\newline$ Divide the leading term of the new expression $7x$ by $x$ to get $7$ . $\newline$ Multiply $7$ by $(x - 1)$ to get $7x - 7$ . $\newline$ Subtract $(7x - 7)$ from $(7x - 4)$ to get $3$ .
Write Final Result: Step $3$ : Write the final result of the division. $\newline$ The quotient from the division is $x + 7$ and the remainder is $3$ . $\newline$ Express the original expression as $p(x) + \frac{k}{x-1}$ where $p(x) = x + 7$ and $k = 3$ .

More problems from Simplify exponential expressions using exponent rules

Question

\newline

2^2 =

Posted 2 months ago

Question

Evaluate. Write your answer as a fraction or whole number.

\newline

(\frac{1}{4})^4

Posted 2 months ago

Question

Which is equal to

9^{-61}

\newline

\newline

\frac{1}{(-9)^{-61}}

\newline

(-9)^{-61}

\newline

(-9)^{61}

\newline

\frac{1}{(9^{61})}

Posted 1 month ago

Question

\newline

Express your answer using positive exponents.

\newline

r^5 \cdot r^8

Posted 2 months ago

Question

Simplify. Express your answer using a single exponent.

\newline

(h^2)^6

\newline

Posted 1 month ago

Question

Simplify. Express your answer using positive exponents.

\newline

(9p^5)(5p^8)

\newline

Posted 2 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

(2v^3)(4v)(5v)

\newline

Posted 2 months ago

Question

Simplify. Express your answer using a single exponent.

\newline

(5z^8)^2

\newline

Posted 2 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

r^9 \cdot r^8 \cdot r^{\text{-}5}

\newline

Posted 2 months ago

Question

Which expression is equivalent to

6 \times 6^8

\newline

\newline

\frac{1}{6^9}

\newline

6^8

\newline

\frac{1}{6^8}

\newline

6^9

Posted 1 month ago