Difference of two squares and the square of a binomial

1. Give an example of a single polynomial with degree 3, whose value is 4 when the variable is equal to 1.

2. Give an example of a single polynomial with degree 3, whose value is 29 when the variable is equal to 2.

3. Find a polynomial with degree 3 whose values are 4 and 29 when the variable is equal to 1 and 2, respectively. How many polynomials that satisfy these constraints are there? Note that in this part, you need to come up with a single polynomial that satisfies these two constraints simultaneously.

4. State the identities of the difference of two squares and the square of a binomial. Why do you think they are important? give at least one example from each identity.

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Give an example of a single polynomial with degree 3, whose value is 4 when the variable is equal to 1.
A general form of single polynomial with degree 3:
Y = ax3 + bx2 + cx + d
Here we need to substitute x = 1. Thus
4 = a + b + c + d
As you can see, there are many solutions to this problem. So we will have to guess for one, say a = b = c = d = 1.
Thus we have the function required:
Y = x3 + x2 + x + 1

Give an example of a single polynomial with degree 3, whose value is ...

Solution Summary

The solution explains in detail the relevant concepts and then provides step-by-step problem-solving instructions in a 4-page Word document.

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... Anova Table Source of Sum of Squares Degrees of Mean square F variation ... We still can't tell where the differences are, but we know we have a difference! ...

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... What is the difference in how each is used to test hypothesis ... goodness-of-fit are used to detect group differences using frequency ... normal chi-square goodness of ...

... 34 The Square of a Binomial. Find the square of each sum or difference (3w - 2x)subscript2. #44 Product of a sum and a difference (3 + 5x)(3 - 5x). ...

... Chi-Squares. ... At alpha significance level of .01, is there a difference in the number of rounds ... but we need to find the magnitude of the differences relative to ...

... To estimate the difference in the two brands, an experiment is conducted ... the tests mentioned in the title are chi-square tests ... The chi-squared test statistic is ...

... 16b 2 (b − c) = (b − c)(a 2 − 16b 2 ) Then using the difference of squares... kn 2 = (3m + 7 n)(3m − 7 n) Using the differences of the squares, we have ...