# Recent questions in Polynomial arithmetic

Polynomial arithmetic

### Show that f is continuous on $$(−\infty, \infty)$$. $$f(x) =1 − x^2 if x \leq 1$$ $$\ln(x) if x > 1$$

Polynomial arithmetic

### (a)To calculate: The value of P(2) without a calculator using both forms of the polynomial. The value of P (2) is 236. (b)The least amount of arithmetic operations was performed in (c) using Horner's method.

Polynomial arithmetic

### Calculate: Polymomial equation with real coefficients taht has roots 3, 1 - i.

Polynomial arithmetic

### Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio. If the sequence is arithmetic or geometric, find the sum of the first 50 terms. $$\{9=\frac{10}{11}n\}$$ What type of sequence is $$9=\frac{10}{11}n$$

Polynomial arithmetic

### The general term of a sequence is given $$a_{n} = \left(\frac{1}{2}\right)^{n}$$. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.

Polynomial arithmetic

### Solve the Numerical Analysis Explain how Newton`s interpolation formula better than the Lagrange formula.

Polynomial arithmetic

### Let $$x_1 = 94,210, x_2 = 8631, x_3 = 1440, x_4 = 133,$$ and $$x5 = 34.$$ Calculate each of the following, using four-digit decimal floating-point arithmetic: $$x1 + ((x2 + x3) + (x4 + x5))$$

Polynomial arithmetic

### Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution. a. $$\frac{1}{3}, \frac{2}{9}, \frac{3}{27}, \frac{4}{81}, ...$$ b. $$3, 8, 13, 18, ..., 48$$

Polynomial arithmetic

### Prove the Fundamental Theorem of Arithmetic. Every integer than 1 is a prime or a product of primes. This product is unique, exept for the order in which the factors appear.

Polynomial arithmetic

### What is an arithmetic sequence? Write a formula for the nth term of an arithmetic sequence.

Polynomial arithmetic

### Determine whether the sequence is arithmetic. If so, identify the common difference 11, 10.2, 9.4, 8.6, 7.8, …

Polynomial arithmetic

### Let $$c = 3.4215298\ \text{and}\ d = 3.4213851$$. Calculate c − d using six-digit decimal floating-point arithmetic.

Polynomial arithmetic

### DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q ae the same $$P(x) = 3x^{4} - 5x^{3} + x^{2} - 3x +5$$ $$Q(x) = (((3x - 5)x + 1)x^3)x + 5$$ Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial $$R(x) =x^{5} - 2x^{4} + 3x^{3} - 2x^{2} + 3x + 4$$ in “nested” form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value ofa polynomial using synthetic division?

Polynomial arithmetic

### Indicate whether the expression defines a polynomial function. $$\displaystyle{P}{\left({x}\right)}=−{x}{2}+{3}{x}+{3}$$ polynomial or not a polynomial If it is a polynomial function, identify the following. (If it is not a polynomial function, enter DNE for all three answers.) (a) Identify the leading coefficient. (b) Identify the constant term. (c) State the degree.

Polynomial arithmetic

### State the fundamental theorem of arithmetic.

Polynomial arithmetic

### Find the probability of the indicated event if $$P(E)=0.25\ and\ P(F)=0.45. P( E\ or\ F ) if E$$ and Fare mutually exclusive

Polynomial arithmetic

### The first four terms of a sequence are given. Can these terms be the terms of an arithmetic sequence? $$38, -22, -6, 10,...$$ Yes, the sequence is arithmetic. No, the sequence is not arithmetic. If the sequence is arithmetic, find the common difference d. (If the sequence is not arithmetic, enter DNE.) $$d=?$$

Polynomial arithmetic

### Consider the following sequence. $$\displaystyle{s}_{{n}}={2}{n}−{1}$$ a) Find the first three terms of the sequence whose nth term is given. $$\displaystyle{s}_{{1}}=$$ $${s}_{{2}}=$$ $${s}_{{3}}=$$ b) Classify the sequence as arithmetic, geometric, both, or neither. arithmeticgeometric bothneither If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.)

Polynomial arithmetic