The Fundamental Theorem of Algebra Sed 33. r(x)= x* +7x² – 41x² +33x 34. d(x)= x³ – x* – 18x' +18x² + 81x – 81 35. P(x)= x³ – 6x² +28x – 40 %3D= 36. g(x)= x° – x*–16x² +16 Construct polynomial functions with the stated properties. See Example 3. of 42. Fifth-degree, -2 is multiplicity 2, another integer is a zero of multiplicity 3, y-intercept is 108, leading coefficient is 1. 37. Third-degree, only real coefficients, -1 and 5+i are two of the zeros, zero y-intercept is –52. 38. Fourth-degree, only real coefficients, V7 and i/5 are two of the zeros, y-intercept is –35. 43. Third-degree, only real coefficients, -4 and 3+i are two of the zeros, y-intercept is –40. 39. Fifth-degree, 1 is a zero of multiplicity 3, –2 is the only other zero, leading 44. Fifth-degree, 1 is a zero of multiplicity 4,-2 is the only other zero, leading coefficient is 4. coefficient is 2. 40. Fifth-degree, only real coefficients, 0 is the only real zero, 1+i is a zero of 45. Third-degree, only real coefficients, multiplicity 1, leading coefficient is 1. -4 and 4+i are two of the zeros, y-intercept is -68. 41. Fourth-degree, only real coefficients, x-intercepts are 0 and 6,-2i is a zero, leading coefficient is 3.

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.