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aleksklad [387]
1 year ago
8

F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2) I need to factor and find the zeros.

Mathematics
1 answer:
Ratling [72]1 year ago
3 0

Answer:

\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)

\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1

Step-by-step explanation:

<u>Given function</u>:

f(x)=3x^3-2x^2-11x+10

If (x + 2) is a factor then:

\implies f(x)=(x+2)(ax^2+bx+c)

Expand:

\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c

\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c

\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c

To find <em>a</em>, compare the coefficients of x³:

\implies a=3

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

\implies 2a+b=-2

\implies 2(3)+b=-2

\implies b=-8

To find <em>c</em>, compare the constants:

\implies 2c=10

\implies c=5

Therefore:

\implies f(x)=(x+2)(3x^2-8x+5)

Now factor (3x²-8x+5):

\implies 3x^2-3x-5x+5

\implies 3x(x-1)-5(x-1)

\implies (3x-5)(x-1)

Therefore the factored function is:

\implies f(x)=(x+2)(3x-5)(x-1)

<u>Zero Product Property</u>

\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}

To find the zeros, set each factor equal to zero and solve for x:

\implies x+2=0 \implies x=-2

\implies 3x-5=0 \implies x=\dfrac{5}{3}

\implies x-1=0 \implies x=1

Therefore, the zeros of the function are:

x=-2, \quad x=\dfrac{5}{3},\quad x=1

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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 7 ft b
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Given:

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Sol:

Volume is:

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The formula of density is:

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So,

\begin{gathered} 0.21=\frac{\text{ Weight  of contents in container}}{\text{ Volume of container}} \\  \\ 0.21=\frac{\text{ Weight}}{297.5} \\  \\ 0.21\times297.5=\text{ Weight} \\  \\ \text{ Weight of contents in container = }62.475\text{ Pound} \end{gathered}

Now $8.80 per pound

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1 year ago
Please give me the ansewer to this question 3/4^3
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♡ The Question ♡

-Answer --> 3/4^3

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Answer ♡

Fraction --> 27/64

Decimal --> 0.421875

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ The Explanation/Step-By-Step ♡

(3/4)^3

Apply Exponent Rule! --> (a/b)^c = a^c/b^c

(3/4)^3 = 3^3/4^3

3^3 = 27

= 27/4^3

4^3 = 64

= 27/64

27/64 = 0.421875

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*

♡ Tips ♡

-No tips provided!

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Step-by-step explanation:

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By definition, Vertical angles are congruent, which means that the have the equal measure.

In this case, you can observe in the picture provided in the exercise that the line TI and the line WN intersect each other at the point S.

You can identify that the pair of angles that are opposite to each other and share the same vertex are the shown below:

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