We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2.

8 0

2 years ago

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Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2

butalik [34]

To solve this question, we use the factor theorem, and using it, the polynomial function is:

$f(x) = x^3 - 2x^2 - 3x + 6$

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The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which: $f(2) = 0, f(\sqrt{3}) = 0, f(-\sqrt{3}) = 0$

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Function 1:

$f(x) = x^3 - 2x^2 - 3x + 6$

Testing the values:

$f(2) = 2^3 - 2(2)^2 - 3(2) + 6 = 8 - 8 - 6 + 6 = 0$

$f(\sqrt{3}) = \sqrt{3^3} - 2(\sqrt{3})^2 - 3\sqrt{3} + 6 = \sqrt{3^2\times3} - 6 - 3\sqrt{3} + 6 = 3\sqrt{3} - 3\sqrt{3} = 0$

$f(-\sqrt{3}) = -\sqrt{3^3} - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 = -\sqrt{3^2\times3} - 6 + 3\sqrt{3} + 6 = -3\sqrt{3} + 3\sqrt{3} = 0$

Thus, since all three conditions are satisfied, $f(x) = x^3 - 2x^2 - 3x + 6$ is the polynomial function.

A similar question is given at brainly.com/question/11378552

5 0

2 years ago

Which is the graph of f(x) = x2 – 2x + 3?

icang [17]

To find the graph of f(x) = x^2 - 2x + 3, you can either plug in values into where the x variable stands and solve for their corresponding y-values or you can also use your graphing calculator or even Desmos works!

3 0

2 years ago

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