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Pani-rosa [81]
3 years ago
12

Help please u can choose more than 1

Mathematics
1 answer:
andrezito [222]3 years ago
5 0

Answer:

\frac{12}{22} and \frac{6}{11}

Step-by-step explanation:

Both \frac{12}{22} and \frac{6}{11} are equal to 0.54 as a repeating decimal

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Zina [86]

Answer:

\displaystyle \frac{1}{2}(x^3-2x^2-5x+6)

Step-by-step explanation:

<u>Polynomials </u>

a)

The polynomial whose graph is shown is of third degree because it has three real roots. The roots of a polynomial are the values of x that make the expression equal to zero. We can see it happens three times in the graph provided. The roots or zeros are  

x=-2, x=1, x=3

b)

The factored form of a polynomial whose roots x_1, x_2, x_3 are known is

a(x-x_1)(x-x_2)(x-x_3)

We know the value of the roots, thus the polynomial is written as

a(x+2)(x-1)(x-3)

We need to find the value of a. We do that by replacing the value of x=0 and finding a that makes f(0)=3 (as seen in the graph). Thus

a(0+2)(0-1)(0-3)=3

a(2)(-1)(-3)=3

a(6)=3

\displaystyle a=\frac{3}{6}

\displaystyle a=\frac{1}{2}

Thus the factored form of the polynomial is

\displaystyle \frac{1}{2}(x+2)(x-1)(x-3)

c)

Let's multiply all the factors

\displaystyle \frac{1}{2}(x+2)(x-1)(x-3)

\displaystyle \frac{1}{2}(x^2+2x-x-2)(x-3)

\displaystyle \frac{1}{2}(x^2+x-2)(x-3)

\displaystyle \frac{1}{2}(x^3-3x^2+x^2-3x-2x+6)

\boxed{ \displaystyle \frac{1}{2}(x^3-2x^2-5x+6)}

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