College Algebra - Assignment Example

Algebra Affiliation Algebra Questions chosen are question 2, 4 and 5 Question 2 The degree of the function x2(x-2)3 canbe determined by first expanding the function and then the terms are put in decreasing order of their exponential. . The function is then expanded as shown below.The expansion of (x-2)3 is first done and the result multiplied by x2 x2(x-2)3 x2(x3- 6x2 + 12x - 8)x5- 6x4 + 12x3 - 8 x2 The coefficients of the function are not necessary for the determination of the degree of the polynomials, therefore they are ignored and the equation rewritten as:x5- x4 + x3 - x2 The power of the largest term is then identified.

For this function, the largest term is the first term with the power of 5.Therefore, the degree of the function is 5 Question 4A graph can be determined if it crosses the x-axis or just touches it by identifying the repeated factors. When a function has a factor which is a multiple of two or an even, then the graph will just touch the x-axis at the point satisfying its roots and will turn around. Therefore, the graph will remain on the same side of the x-axis.An example of a function with repeated factors (even multiplicity) is: x2 +6x + 9 with repeated factors (x + 3)2, therefore, it touches the x-axis only at point x= -3 and does not cross the x-axis as shown in the graph below.

When a function has a factor which is a multiple of three or odd, then the graph will just cross the x-axis at the point satisfying its roots. An example of a function with triple factors (odd multiplicity) is: x3 -3x2 +3x - 1 with repeated factors (x - 1)3, therefore, it crosses the x-axis only at point x= 1 as shown in the graph below.Question 3The turning point of a graph is the point that a graph changes direction form decreasing to increasing or from increasing to decreasing. Turning points can also show the maximum point, minimum point and point of inflection.

To determine the number of turning point, the degree of polynomial is lessened by one (n - 1) where n is the degree of polynomial; therefore the turning point of its graph is always less than the degree of the polynomial. For example, a polynomial of degree 4 will have 3 turning points or even less as can be seen in the two graphs below.A polynomial of the function; x4 – 2x2 + x, has 3 turning points as shown below.A polynomial of the function; x4 – 2x, has only one turning points as shown below.

ReferencesSidney L., Annette M., Li A. & Barbara J. (2001). Algebra I: A Process Approach (Student Text). Hawaii, USA: CRDG.