Question

1. divide $6x^{4}+25x^{3}+4x$ by $-5x$
2. simplify $(7s^{2}-2s+8)+(s^{2}+3s)$

Explanation:

Problem 6

Step1: Split the polynomial division

$\frac{6x^4 + 25x^3 + 4x}{-5x} = \frac{6x^4}{-5x} + \frac{25x^3}{-5x} + \frac{4x}{-5x}$

Step2: Simplify each term

$\frac{6x^4}{-5x} = -\frac{6}{5}x^3$, $\frac{25x^3}{-5x} = -5x^2$, $\frac{4x}{-5x} = -\frac{4}{5}$

Step3: Combine simplified terms

$-\frac{6}{5}x^3 -5x^2 -\frac{4}{5}$

Step1: Remove parentheses

$7s^2 - 2s + 8 + s^2 + 3s$

Step2: Combine like terms

$(7s^2 + s^2) + (-2s + 3s) + 8$

Step3: Simplify each like term group

$8s^2 + s + 8$

Answer:

$-\frac{6}{5}x^3 - 5x^2 - \frac{4}{5}$

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Problem 7