Please help!!! Will give 20 points if right! Need ASAP!!
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Answer:
x < -3 or x > 4
Step-by-step explanation:
The product of the factors is 4th-degree, and the leading coefficient is 1 (positive).
The factors tell you the following about the zeros:
x = -3 . . . sign change from + to -
x = -1 . . . graph touches, but no sign change. - on either side of x=-1
x = 4 . . . sign change from - to +
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The function will be positive for x < -3 and for x > +4.
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<em>Additional comments</em>
The value of the function is zero when any of its factors is zero. The value of a factor changes sign when the value of x changes from one side of the 0 to the other. For example, here, we have x+1 as a factor, so x=-1 is a zero. When x = -0.9, the factor is positive (-0.9 +1 = 0.1). When x = -1.1, the factor is negative (-1.1 +1 = -0.1). If this factor were to the first power, it would cause the value of the function to change sign at x=-1.
However, the factor (x+1) has an even power: (x+1)^2. That means when the factor is negative, its square is positive, and when the factor is positive, its square is positive. In short, the factor (x+1)^2 causes the function to be zero at x=-1, but does not make the function change sign there.
The product of all of these factors will result in a polynomial with x^4 as the highest-degree term. That means the function is of even degree. The leading coefficient is 1, so is positive, and the function will generally have a U-shape. The left-most (odd-degree) zero will be where the function changes sign from positive to negative. The right-most (odd-degree) zero will be where the function changes sign from negative to positive. Those zeros are x=-3 and x=+4, respectively. There are no places between these where the function changes sign, so these zeros are the ends of the regions where the function is positive (>0).
Answer: 3, then 5/8, then, -2.9, and finally -4.
Step-by-step explanation:
3 is the biggest positive integer in value, so that one is automatically first.
5/8 is the second-biggest positive number in value. It isn't a full number, considering it is a fraction, but it is a positive number nonetheless so that makes it larger in value than the last two:
-2.9 is the third-largest integer in value, leaving -4 as the smallest number in this sequence. I know, I know, you're probably like "but 4 is bigger than 2.9." Let me explain the logistics behind this.
When figuring out which number is larger and which is smaller with negative integers, you go by how far they are from 0 on a number line. -2.9 is 2.9 places from zero on a number line. This is called absolute value. Absolute value is defined as "how far a number is on a number line from zero." The absolute value of -4 is 4. (Absolute value is ALWAYS positive). As you can see from this simple observation, -4 is farther from -2.9 on a number line and is therefore less than -2.9. Using the absolute values of negative integers, classifying them from least to greatest or greatest to least is fairly easy. Hopefully this helped. :)
