Question 151967: 1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1.
2. Using FOIL, simplify the expression "(3x + 2)(3x - 2)". Show that a particular factoring formula leads to the same answer.
3. If a fourth-degree polynomial is multiplied by a third-degree polynomial, what is the degree of the product? Explain your reasoning and provide examples to support your explanation.
4. Think of a condition under which the product of any two binomials is a binomial. You can support your answer with the help of one of the identities of factorization of polynomials.
5. (i) Is "12.5555…" a rational or irrational number? Explain.
(ii) Is "2.1273685…" a rational or irrational number? Explain.
(iii) Is "548/799" a rational or irrational number? Explain.
(iv) Simplify "(5 + 3i)(5 - 3i)". Is the result real, complex, or both? Explain.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1.
n^x/n^x = 1 because anything, except zero, divided by itself is one.
But n^x/n^x = n^(x-x) = n^0 by the division law of exponents.
Therefore n^0 must equal 1 for all n that is not equal to zero.
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2. Using FOIL, simplify the expression "(3x + 2)(3x - 2)".
F: 3x*3x = 9x^2
O: 3x*-2 = -6x
I: 2*3x = 6x
L: 2*-2 = -4
Combine to get: 9x^2 -4
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Show that a particular factoring formula leads to the same answer.
(a+b)(a-b) = a^2 - b^2 is the form for the difference of squares.
In your problem a = 3x and b = 2
So you have (3x+2)(3x-2) = (3x)^2-2^2 = 9x^2-4
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3. If a fourth-degree polynomial is multiplied by a third-degree polynomial, what is the degree of the product?
seven
Explain your reasoning and provide examples to support your explanation.
(x^4-1)(x^3-1) = x^7-x^4-x^3+1
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4. Think of a condition under which the product of any two binomials is a binomial. You can support your answer with the help of one of the identities of factorization of polynomials.
(a+b)(a-b) = a^2-b^2
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5. (i) Is "12.5555…" a rational or irrational number? Explain.
rational because is has a repeating decimal form.
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(ii) Is "2.1273685…" a rational or irrational number? Explain.
It appears to have a non-repeating decimal form so it is irrational.
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(iii) Is "548/799" a rational or irrational number? Explain.
rational because it is the ratio of two integers.
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(iv) Simplify "(5 + 3i)(5 - 3i)". Is the result real, complex, or both? Explain.
= 5^2 - (3i)^2 = 25 +9 = 34 which is rational.
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Cheers,
Stan H.
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