Answer:
[tex]\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4} = x^2 + 5x - 4 + \frac{3x - 8}{x^2 + 5x - 4}[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Algebra II
Polynomial Division
- Long Division
- Synthetic Division
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4}[/tex]
Step 2: Long Division
See attachment.
- Multiply quotient a and divisor, then subtract from dividend: [tex]\displaystyle x^2(x^2 + 5x - 4) = x^4 + 5x^3 - 4x^2 \leftarrow \text{red 1}[/tex]
- Multiply quotient b and divisor, then subtract from new dividend: [tex]\displaystyle 5x(x^2 + 5x - 4) = 5x^3 + 25x^2 - 20x \leftarrow \text{red 2}[/tex]
- Multiply quotient c and divisor, then subtract from new dividend: [tex]\displaystyle 4(x^2 + 5x - 4) = 4x^2 + 20x - 16 \leftarrow \text{red 3}[/tex]
- Write remainder: [tex]\displaystyle \frac{r(x)}{b(x)} = \frac{3x - 8}{x^2 + 5x - 4}[/tex]
Please excuse the bad handwriting.
