Hello I need help

2 answers:

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6 0

Answer:

here is the answer

Step-by-step explanation:

here is the explanation

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almond37 [142]

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Step-by-step explanation:

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Lapatulllka [165]

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Tju [1.3M]

Answer:

$\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4} = x^2 + 5x - 4 + \frac{3x - 8}{x^2 + 5x - 4}$

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Algebra II

Polynomial Division

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4}$

Step 2: Long Division

See attachment.

Multiply quotient a and divisor, then subtract from dividend: $\displaystyle x^2(x^2 + 5x - 4) = x^4 + 5x^3 - 4x^2 \leftarrow \text{red 1}$
Multiply quotient b and divisor, then subtract from new dividend: $\displaystyle 5x(x^2 + 5x - 4) = 5x^3 + 25x^2 - 20x \leftarrow \text{red 2}$
Multiply quotient c and divisor, then subtract from new dividend: $\displaystyle 4(x^2 + 5x - 4) = 4x^2 + 20x - 16 \leftarrow \text{red 3}$
Write remainder: $\displaystyle \frac{r(x)}{b(x)} = \frac{3x - 8}{x^2 + 5x - 4}$