# Chapter 5 - Review Exercises - Page 416: 67

$$-6x^5 + 5x^4 + 8x^2$$

#### Work Step by Step

Taking a look at the numerator of this rational expression, we see that the factor $5x^5$ is common to all three terms, so $5x^5$ is called the greatest common factor. We can simplify this expression by factoring out the greatest common factor to get: $$\frac{5x^5(6x^3 - 5x^2 - 8)}{-5x^3}$$ We can cancel out a $5x^3$ from the numerator and denominator, leaving $-x^2$. We now have: $$-x^2(6x^3 - 5x^2 - 8)$$ We use the distributive property to multiply the first factor $-x^2$ by each of the terms in the trinomial to get: $$(-x^2)(6x^3) + (-x^2)(-5x^2) + (-x^2)(-8)$$ Multiply out the terms using the product rule of exponents, which states that if you multiply two powers with the same base, you can add the two bases together and keep the same base: $$-6x^5 + 5x^4 + 8x^2$$

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