Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial, write and factor the trinomial. x^2−3x.

Question
Polynomials
asked 2020-12-25
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial, write and factor the trinomial.
\(\displaystyle{x}^{{2}}−{3}{x}.\)

Answers (1)

2020-12-26
The coefficient of the x-term in \(\displaystyle“{x}^{{2}}–{3}{x}”\) is “-3”
Half of “-3” is \(\displaystyle-\frac{{3}}{{2}}{\quad\text{and}\quad}{\left(-\frac{{3}}{{2}}\right)}^{{2}}=\frac{{9}}{{4}}\), then
\(\displaystyle{x}^{{2}}–{3}{x}+\frac{{9}}{{4}}={\left({x}–\frac{{3}}{{2}}\right)}^{{2}}\)
The answer is \(\displaystyle\frac{{9}}{{4}},{\left({x}–\frac{{3}}{{2}}\right)}^{{2}}\)
0

Relevant Questions

asked 2021-01-19
Factor the trinomial. Note that the coefficient of \(\displaystyle{x}^{{2}}\) is not equal to 1. \(\displaystyle{4}{x}^{{2}}–{3}{x}={10}.\)
asked 2020-11-27
Fill in each blank so that the resulting statement is true. "After performing polynomial long division, the answer may be checked by multiplying the ____ by the ____, and then adding the ____. You should obtain the ____."
asked 2020-11-08
A resort is situated on an island that lies exactly 4 miles from P, the closest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the nearest source of water. If it costs 1.6 times as much money to lay pipe in the water as it does on land, how far down the shoreline from P should the pipe from the island reach land with minimum total constructions costs?
asked 2021-01-31
factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 70 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.
(a) What is the level of significance?
State the null and alternate hypotheses.
\(H_{0}:\sigma=60,\ H_{1}:\sigma\ <\ 60H_{0}:\sigma\ >\ 60,\ H_{1}:\sigma=60H_{0}:\sigma=60,\ H_{1}:\sigma\ >\ 60H_{0}:\sigma=60,\ H_{1}:\sigma\ \neq\ 60\)
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
What assumptions are you making about the original distribution?
We assume a binomial population distribution.We assume a exponential population distribution. We assume a normal population distribution.We assume a uniform population distribution.
asked 2021-01-13
write the polynomial \(\displaystyle{P}{\left({x}\right)}={x}^{{{2}}},\) if possible as a linear combination of the polynomials \(\displaystyle{1}+{x},{2}+{x}^{{{2}}},−{x}.\)
asked 2021-01-31
Please, factor this polynomial: x^3 + 1
asked 2020-10-28
Determine the algebraic modeling a.
One type of Iodine disintegrates continuously at a constant rate of \(\displaystyle{8.6}\%\) per day.
Suppose the original amount, \(\displaystyle{P}_{{0}}\), is 10 grams, and let t be measured in days.
Because the Iodine is decaying continuously at a constant rate, we use the model \(\displaystyle{P}={P}_{{0}}{e}^{k}{t}\) for the decay equation, where k is the rate of continuous decay.
Using the given information, write the decay equation for this type of Iodine.
b.
Use your equation to determine the half-life ofthis type of Fodine, That is, find ‘out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs.
asked 2020-11-26
A bag contains 6 red, 4 blue and 8 green marbles. How many marbles of each color should be added so that the total number of marbles is 27, but the probability of randomly selecting one marble of each color remains unchanged.
asked 2021-01-27
Factor the polynomial 25t^2 + 90t + 81
asked 2020-12-16
Factor the polynomial t^6 – 125
...