College Algebra Exercises Section 3.3
As
you study these exercises, move your cursor over the light bulbs and the highlighted
words.
Study with an active cursor
The definition that pops up when you move the cursor over a highlighted word is what should pop into your mind when you read, hear, or speak that word. | The material that pops up when you move the cursor over a light bulb is a suggested strategy for solving the problem. You should always formulate a similar strategy when you attempt to solve a problem. | When you move the cursor over an explanation of a step in a solution, the property that pops up is the mathematical justification for taking that action. You must always be able to provide such a justification for every step you take in mathematics. |
6) Use long division to find the quotient and remainder when 5x^{2} -17x -12 is divided by x - 4.
Solution:
What can we conclude from this?
This process has revealed the quotient 5x + 3 and remainder 0 as assured by the Division Algorithm.
Now we know
5x^{2} - 17x -12 = (x - 4)(5x + 3)
With this factorization and the Zero Factor Property we can easily determine that the zeros of the function f whose rule is f(x) = 5x^{2} - 17x -12 are 4 and .
Since both of these zeros are real numbers, they are x-intercepts of the function f.
The graph of the function f is clearly a parabola which opens up and crosses the x-axis at 4 and
All that remains to completely determine the graph of f is to compute the vertex using the formula
Remark: For a quadratic function we do not go to all this effort. It is done here only as an example of what can be interpreted from a division problem.
8) Use long division to find the quotient and remainder when 6x^{3} - 16x^{2} + 17x - 6 is divided by 3x - 2.
Remark: We now know one x-intercept. |
9) Use long division to find the quotient and remainder when x^{4} + 5x^{3} + 6x^{2} -x - 2 is divided by x+ 2.
Remark: We now know one x-intercept. |
42) Use long division to find the quotient and remainder when x^{3} + 2x^{2} - 5x - 4 is divided by x+ . |
73) Use long division to find the quotient and remainder when x^{4} + 6x^{3} + 11x^{2} + 6x is divided by x^{2} +3x+ 2. |
EXTRA) Use long division to find the quotient and remainder when is divided by . |