Question
Studdy Solution
STEP 1
What is this asking?
We're diving into polynomial division!
We need to divide the polynomial by .
Watch out!
Keep your signs straight and remember to multiply correctly during each step.
It's easy to slip up, so double-check your work!
STEP 2
1. Set up the long division.
2. Divide the leading term.
3. Multiply and subtract.
4. Bring down the next term.
5. Repeat.
STEP 3
Alright, let's **set up** our long division problem just like we'd do with regular numbers!
We put the **dividend**, , inside the long division symbol and the **divisor**, , outside.
STEP 4
Now, we **divide** the leading term of the dividend, , by the leading term of the divisor, . divided by is .
We write this **result** above the division symbol.
STEP 5
Next, we **multiply** our by the entire divisor, , which gives us .
We write this **product** below the dividend and **subtract** it.
STEP 6
We **bring down** the next term of the dividend, which is .
STEP 7
We **repeat** the process.
Divide the leading term by the leading term of the divisor, which gives us .
Write this above the division symbol.
STEP 8
Multiply by the divisor to get .
Subtract this from .
\begin{array}{c c c c}
x+4 & 5x^2 & -x & -9 \\
& 5x^2 & +20x & \\
\cline{2-3}
& 0 & -21x & -9 \\
& & -21x & -84 \\
\cline{3-4}
& & 0 & 75 \\
\end{array}
STEP 9
Our **quotient** is and our **remainder** is .
We can write the final answer as .
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