Factor completely 3X^2 -25

Mathematics

1 answer:

Dominik [7]2 years ago

5 0

In order to factor a polynomial, you have to find its roots

$x_1,\ x_2,\ldots,x_n$

So that you can factor it as

$p(x)=(x-x_1)(x-x_2)\cdots(x-x_n)$

So, in this case, we're looking for the solutions of

$3x^2-25=0 \iff 3x^2=25 \iff x^2 = \dfrac{25}{3} \iff x=\pm\sqrt{\dfrac{25}{3}}=\pm\dfrac{5}{\sqrt{3}}$

So, the polynomial can be written as

$3x^2-25 = \left(x-\dfrac{5}{\sqrt{3}}\right)\left(x+\dfrac{5}{\sqrt{3}}\right)$

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See the attachment.

Step-by-step explanation:

Function notation: This means the description of the curve is written in the form ...

f(x) = <an expression that describes the curve in terms of independent variable x>

The name of the function does not have to be "f", though f, g, h are traditional for generic functions. In specific cases, the function name might be related to the value the function delivers: <em>cost(n)</em> might be the function that tells you the cost of producing n items, for example.

The functions shown (square root, reciprocal) should be shapes you have memorized. You can check the scale factor at specific values you know, for example, √4 = 2, or 1/1 = 1. Hence both functions have a scale factor of 1 (no scaling).

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The domain is the horizontal region where the function is defined. Square root is not defined for negative numbers; reciprocal is not defined for 0. Hence the descriptions of the respective domains must exclude these values.

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The range is the vertical extent of the values each function produces. The domain and range are the same for both functions shown here.

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Asymptotes are lines the function approaches but does not reach. The square root function has no such lines. (It reaches vertical at x=0.)

The reciprocal function has a vertical asymptote as x=0 (the value of x that makes the function denominator zero). And, it has a horizontal asymptote at y=0, a value that can be approached, but not reached, as x gets large in either the positive or negative directions.

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End behavior: The square root function heads off toward (∞, ∞). The reciprocal function heads toward the value defined by the horizontal asymptote: y=0 as x gets large in magnitude.