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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 ITerms/CoefficientsExpandingAlgebra IIPolynomial DivisionLong DivisionSynthetic DivisionStep-by-step explanation:Step 1: DefineIdentify.[tex]\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4}[/tex]Step 2: Long DivisionSee 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.