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3 years ago

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If f(x)=2x²+5√(x-2) , complete the following statement: f(3)=___

1 answer:

aliya0001 [1]3 years ago

4 0

F(x)=2x²+5√(x-2)

f(3)=2(3)²+5√(3-2)
= 2 (9) + 5√1
= 18 + 5
= 23.

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Question 14 of 25What is the complete factorization of the polynomial below?x³+x² + 4x+4O A. (x-1)(x+2)(x+2)B. (x + 1)(x + 2)(x

mote1985 [20]

GIVEN:

We are given the following polynomial;

$x^3+x^2+4x+4$

Required;

We are required to factorize this polynomial completely.

Step-by-step explanation;

To factorize this polynomial, we start by grouping;

$(x^3+x^2)+(4x+4)$

We now take the common factor in each group;

$\begin{gathered} x^2(x+1)+4(x+1) \\ \\ (x^2+4)(x+1) \end{gathered}$

Next, we factorize the first parenthesis. To do this we set the equation equal to zero and solve for x as follows;

$\begin{gathered} x^2+4=0 \\ \\ Subtract\text{ }4\text{ }from\text{ }both\text{ }sides: \\ \\ x^2=-4 \\ \\ Take\text{ }the\text{ }square\text{ }root\text{ }of\text{ }both\text{ }sides: \\ \\ x=\pm\sqrt{-4} \\ \\ x=(\pm\sqrt{-1}\times\sqrt{4}) \\ \\ x=\pm2i \end{gathered}$

Therefore, the factors of the other parenthesis are;

$(x+2i)(x-2i)$

Therefore, the complete factorization of the polynomial is;

ANSWER:

$(x+1)(x+2i)(x-2i)$

Option C is the correct answer.

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1 year ago

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kondor19780726 [428]

Answer:

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Step-by-step explanation:

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3 years ago

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Leya [2.2K]

Answer: Option a.

Step-by-step explanation:

1. You have the following parent function given in the problem above:

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$y=f(x+3)-2=(x+3)^{3}-2$ (The function is shifted 2 units down on the y-axis).

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Marizza181 [45]

With some simple rearrangement, we can rewrite the numerator as

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Then factorizing the difference of squares, $x^2-1=(x-1)(x+1)$ , we end up with

$\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}$

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2 years ago