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kakasveta [241]
3 years ago
12

Factor 4a2 - 25. Type your answer in the space provided. Type your answer in the space provided. Do not type spaces in your answ

er. Use only lowercase letters and include all necessary parentheses, variables and operation signs. For example, if the answer is (x +1)(x+2), type (x+1)(x+2).
Mathematics
1 answer:
Dvinal [7]3 years ago
8 0

Answer: The answer to this question is (2a-5)(2a+5)

Step-by-step explanation:

  • Because first,  you have to write the quadratic equation 4a^2-25 in exponential form

  •  Then, you calculate the product by multiplying the terms with equal exponents by multiplying their bases

      (2a)^2-5^2

  •     And then last but not least, using a^2-b^2=(a-b)(a+b), factor the expression

    (2a-5)(2a+5) and then there's your answer and your explanation!!!!!

         

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Find a third degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.
Tanzania [10]

Answer:

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is p(x) = x^{3}-5\cdot x^{2}-6\cdot x.

Step-by-step explanation:

From Fundamental Theorem of Algebra, we remember that the degree of the polynomials determine the number of roots within. Since we know three roots, then the factorized form of the polynomial function with the lowest degree is:

p(x) = (x-r_{1})\cdot (x-r_{2})\cdot (x-r_{3}) = 0 (1)

Where r_{1}, r_{2} and r_{3} are the roots of the polynomial.

If we know that r_{1} = -1, r_{2} = 0 and r_{3} = 6, then the polynomial function in factorized form is:

p(x) = (x+1)\cdot x \cdot (x-6) (2)

And by Algebra we get the standard form of the function:

p(x) = x\cdot (x+1)\cdot (x-6)

p(x) = x\cdot (x^{2}-5\cdot x -6)

p(x) = x^{3}-5\cdot x^{2}-6\cdot x (3)

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is p(x) = x^{3}-5\cdot x^{2}-6\cdot x.

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