A single serving of jello requires 1/8 cups of sugar. How much sugar is needed for 6 servings?
2 answers:
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Subtract 14x from both sides to get
Subtract 12 from both sides to get
Now we have moved all terms involving x on one side, and all constant terms on the other. We can simplift both sides, i.e. sum like terms, to get
Now we have to divide both sides by 6. When dealing with inequality you have to be careful about dividing both sides by the same constant: if the constant is negative, the inequality side switches (i.e. ). But this is not the case since 6 is positive, so we mantain the inequality sign:
on the other. We can simplift both sides, i.e. sum like terms, to get
Evaluate left and right hand side:
Answer:
- zeros: x = -3, -1, +2.
- end behavior: as x approaches -∞, f(x) approaches -∞.
Step-by-step explanation:
I like to use a graphing calculator for finding the zeros of higher order polynomials. The attachment shows them to be at x = -3, -1, +2.
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The zeros can also be found by trial and error, trying the choices offered by the rational root theorem: ±1, ±2, ±3, ±6. It is easiest to try ±1. Doing so shows that -1 is a root, and the residual quadratic is ...
x² +x -6
which factors as (x -2)(x +3), so telling you the remaining roots are -3 and +2.
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For any odd-degree polynomial with a positive leading coefficient, the sign of the function will match the sign of x when the magnitude of x gets large. Thus as x approaches negative infinity, so does f(x).
