FInd the zeroes of the polynomials p(x)=x^2+5x+6

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asked 2021-02-08

Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q ae the same \(\displaystyle{P}{\left({x}\right)}={3}{x}^{{4}}-{5}{x}^{{3}}+{x}^{{2}}-{3}{x}+{5}{N}{S}{K}{Q}{\left({x}\right)}={\left({\left({\left({3}{x}-{5}\right)}{x}+{1}\right)}{x}-{3}\right)}{x}+{5}\) Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial \(\displaystyle{R}{\left({x}\right)}={x}^{{5}}—{2}{x}^{{4}}+{3}{x}^{{3}}—{2}{x}^{{3}}+{3}{x}+{4}\) 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?

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asked 2021-02-21

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?

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asked 2020-10-28

(a)To calculate: The following equation {[(3x + 5)x + 4]x + 3} x + 1 = 3x^4 + 5x^3 + 4x^2 + 3x + 1 is an identity, (b) To calculate: The lopynomial P(x) = 6x^5 - 3x^4 + 9x^3 + 6x^2 -8x + 12 without powers of x as in patr (a).

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asked 2020-12-25

Polynomial equation with real coefficients that has the roots \(3, 1 -i \texr{is} x^{3} - 5x^{2} + 8x - 6 = 0.\)

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asked 2020-12-28

An experiment on the probability is carried out, in which the sample space of the experiment is
\(S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.\)
Let event \(E={2, 3, 4, 5, 6, 7}, event\)
\(F={5, 6, 7, 8, 9}, event G={9, 10, 11, 12}, and event H={2, 3, 4}\).
Assume that each outcome is equally likely. List the outcome s in For G.
Now find P( For G) by counting the number of outcomes in For G.
Determine P (For G ) using the General Addition Rule.

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asked 2020-12-09

Determine whether the following state-ments are true and give an explanation or counterexample.
a) All polynomials are rational functions, but not all rational functions are polynomials.
b) If f is a linear polynomial, then \(\displaystyle{f}\times{f}\) is a quadratic polynomial.
c) If f and g are polynomials, then the degrees of \(\displaystyle{f}\times{g}\) and \(\displaystyle{g}\times{f}\) are equal.
d) To graph \(\displaystyle{g{{\left({x}\right)}}}={f{{\left({x}+{2}\right)}}}\), shift the graph of f 2 units to the right.

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asked 2020-10-20

Write the polynomials as the product of linear factors and list all the zeros of the function.\(h(x) = x^{3}-3x^{2}+4x-2\)

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asked 2020-10-28

Let's calculate the following exponential probability density function.
\(f(x) = \frac{1}{8} e^{x/8} for x \geq 0\)
a.Find \(P(x \leq 4)\)
b.Find \(P(x \leq 6)\)
с.Find \(P(x \geq 6)\)
d.Find \(P(4 \leq x \leq 6)\)

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asked 2020-12-17

For each of the following sequences: @ identify if the sequence is arithmetic, geometric or quadratic’. Justify your response. @ assuming the first item of each sequence is a1, give an expression for aj. (In other words, find a formula for the i-th term in the sequence). @ if the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence \(i 2,-12, 72, -432, 2592,...\)
\(ii 9, 18, 31, 48, 69, 94,...\)
\(iii 14, 11.5, 9, 6.5, 4, 1.5,...\)

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asked 2020-11-23

1. Explain with numerical examples what Real Numbers and Algebraic Expressions are. 2. Explain with numerical examples Factoring and finding LCMs (least common multiples). Explain factoring of a larger number. 3. Explain with numerical examples arithmetical operations (addition, subtraction, multiplication, division) with fractions 4, Explain with numerical examples arithmetical operations (addition, subtraction, multiplication, division) with percentages 5. Explain with numerical examples exponential notation 6. Explain with numerical examples order (precedence) of arithmetic operations 7. Explain with numerical examples the concept and how to find perimeter, area, volume, and circumference (use related formulas)

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Answer 1

Step 1
Given:
\(\displaystyle{p}{\left({x}\right)}={x}^{{2}}+{5}{x}+{6}\)
WKT
Step 2
WKT
To find the zeroes \(\displaystyle{p}{\left({x}\right)}={0}\)
\(\displaystyle{x}^{{{2}}}+{5}{x}+{6}={0}\)
\(\displaystyle{x}{\left({x}+{3}\right)}+{2}{\left({x}+{3}\right)}={0}\)
\(\displaystyle{\left({x}+{3}\right)}{\left({x}+{2}\right)}={0}\)
\(\displaystyle{x}=-{3},\ {x}=-{2}\)
The zeroes of \(\displaystyle{p}{\left({x}\right)}\) are -3 and -2

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FInd the zeroes of the polynomials p(x)=x^2+5x+6

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