Compare the box plots for two data sets.<br> Which statement is true?

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

natka813 [3]

Answer:

x + 3 is a factor of the polynomial.

Step-by-step explanation:

We have been given that p(x) is a polynomial with integer coefficient.

Also p(-3)=0

Since, p(-3) =0, hence, we can say that -3 is a zero of the polynomial.

Now, we apply factor theorem.

Factor Theorem: If 'a' is a zero of a function f(x) then (x-a) must be a factor of the function f(x).

Applying this theorem, we can say that (x+3) must be a factor of the polynomial.

Hence, first statement must be true.

5 0

3 years ago

Read 2 more answers

Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!

Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

$\frac{3}{x + 4} - \frac{1}{x + 3} = \frac{x + 9}{(x^2 + 7x + 12)}$

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

$\frac{3*(x + 4)}{x + 4} - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

$3 - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x + 3)

$3*(x + 3) - \frac{(x + 4)*(x+3)}{x + 3} = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$3*(x + 3) - (x + 4) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$(2*x + 5) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x^2 + 7*x + 12)

$(2*x + 5)*(x^2 + 7x + 12) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)$

$(2*x + 5)*(x^2 + 7x + 12) = (x + 9)*(x + 4)*(x+3)$

Now we need to solve this:

we will get

$2*x^3 + 19*x^2 + 59*x + 60 = (x^2 + 13*x + 3)*(x + 3)$

$2*x^3 + 19*x^2 + 59*x + 60 = x^3 + 16*x^2 + 42*x + 9$

Then we get:

$2*x^3 + 19*x^2 + 59*x + 60 - ( x^3 + 16*x^2 + 42*x + 9) = 0$

$x^3 + 3x^2 + 17*x + 51 = 0$

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

$x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0$

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

6 0

3 years ago

What is the answer???<br> P-6+2=-4+10

miskamm [114]

Answer:p=6-2-4+10

P=4-4+10

P=10

Step-by-step explanation:

3 0

4 years ago

From the set {80, 19, 11}, use substitution to determine which value of x makes the equation true. 8x = 88 A. none of these B. 1

mel-nik [20]

Answer:

C. 11

Step-by-step explanation:

Substituting, we have ...

8{80, 19, 11} ?= 88

{640, 152, 88} ?= 88

The value from the set that makes the equation true is x = 11.

_____

<em>Alternate methods of solution (other than substitution)</em>

It can be easier to make use of your knowledge of factoring:

8x = 8·11

x = 11

Or to make use of your knowledge of numbers (place value):

8·10 = 80

so x will not be very different from 10.

3 0

3 years ago

Determine the factors of x2 − 8x − 12. (x − 6)(x 2) (x 3)(x − 4) prime (x 6)(x − 2)

Ivanshal [37]

The polynomial cannot be factored in because it exists prime. Since 112 exists not a perfect square number so we cannot estimate the factors of the given equation.

<h3>What is a quadratic equation?</h3>

In a quadratic equation ax² + bx + c = 0

when (b² - 4ac) exists a perfect square only then we can factorize the equation.

In the given equation x² - 8x - 12 we have to determine the value of

b² - 4ac

From the equation, we get b = -8 and c = -12

b²- 4ac = (-8)² - 4(1)(-12)

= 64 + 48 = 112

Since 112 exists not a perfect square number so we can not estimate the factors of the given equation.

To learn more about quadratic equation refer to:

brainly.com/question/1214333

#SPJ4

4 0

2 years ago

Compare the box plots for two data sets. Which statement is true?