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3 years ago

P(x) is a polynomial with integer coefficients and p(3) = 0.

Mathematics

1 answer:

Mamont248 [21]3 years ago

4 0

Answer:

The answer is below

Step-by-step explanation:

P(x) is a polynomial with integer coefficients and p(-3) = 0.

Which statements must be true? Choose all that apply.

x + 3 is a factor of the polynomial.

x - 3 is a factor of the polynomial.

-3 is the constant term of the polynomial.

p(x) can have at most 3 linear factors.

Solution:

Polynomial is an expression composed of variables, constants and exponents linked together by mathematical operations (addition, subtraction, multiplication and division)

Given that:

p(-3) = 0.

Since P(-3) = 0, this means that -3 is a factor of the polynomial. Hence:

The factor theorem states that states that if f(a) = 0, therefore a is a factor of the polynomial and hence (x - a) is a factor of polynomial f(x).

Therefore using the factor theorem, we get that x + 3 is a factor of the polynomial.

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Imaginen que un maratonista corre toda una carrera a una velocidad constante. Después de dos horas lleva recorridos 22 km

saw5 [17]

For this case we have:

If after 2 hours the marathon runner has traveled 22 kilometers we have:

2h -----------> 22km

Applying a rule of three, we can know the time it takes to run 42km. So, we have:

2h -----------> 22km

x -------------> 42km

Where "x" is the time it takes to travel 42km. Resolving we have:

$x = \frac {(42 * 2)} {22}$

$x = \frac {84} {22}$

$x = \frac {42} {11}$

$x = 3.82 hours$

Thus, after 3.82 hours the marathon runner will travel 42km.

Answer:

3.82 hours

6 0

3 years ago

What is the y-value of the vertex of the function f(x)=−(x−3)(x+11)? −8 −4 33 49

alisha [4.7K]

Answer:

y - value of the vertex is 49.

Step-by-step explanation:

Given function is f(x) = -(x - 3)(x + 11)

f(x) = -(x² - 3x + 11x - 33)

= -(x² + 8x - 33)

= -(x² + 8x + 16 - 49)

= -[(x + 4)² - 49]

= -(x + 4)² + 49

Comparing this equation with the vertex form of a quadratic function,

f(x) = -(x - h)² + k

Where (h, k) is the vertex of the function.

Vertex of the parabola is (-4, 49)

Therefore, y-value of the vertex is 49.

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3 years ago

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Lemur [1.5K]

Answer:

.....................

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3 years ago

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kodGreya [7K]

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4 years ago

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A sphere has radius of 3 cm. What is the volume of the sphere?

Alex17521 [72]

Answer: 113.04 cm³

Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere which is shown below.

$V = \frac{4}{3} \pi r^{3}$

Here, we are given that our sphere has a radius of 3 centimeters.

So plugging into the formula, we have $(\frac{4}{3})(\pi)(3 cm)^{3}$ .

Start by simplifying the exponent.

(3 cm)³ is equal to 3 centimeters · 3 centimeters ·

3 centimeters or 27 cm³.

So we have $(\frac{4}{3})(27 cm^{3})(\pi)$ .

Notice that we can cross-cancel 3 and 27 to 1 and 9.

So we have (4)(9 cm³) which is equal to 36 cm³.

So we have 36π cm³.

So the volume of the sphere is 36π cm³.

Remember that π is approximately equal to 22/7 or 3.14 so we can estimate the value of the volume by plugging in 3.14 for π.

So we have (36)(3.14) which is equal to 113.04 which means

that the volume of approximately equal to 113.04 cm³.

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3 years ago