Please do correctly! I will mark you Brainliest!

Answer:

We know that P(x) = 30*x^3 + k*x^2 + 1

a) If (3x - 1) is a factor, let's find the value of k.

Because the degree of the original polynomial is 3, and the degree of the factor is 1, we should multiply it by a polynomial of degree 2.

Then:

30*x^3 + k*x^2 + 1 = (3*x - 1)*(a*x^2 + b*x + c)

30*x^3 + k*x^2 + 1  = 3*a*x^3 + 3*b*x^2 + 3*c*x - a*x^2 - b*x - c

30*x^3 + k*x^2 + 1 = 3*a*x^3 + (3*b - a)*x^2 + (3*c - b)*x - c

The terms with the same exponent should be equal, then:

30*x^3 = 3*a*x^3

30 = 3*a

30/3 = a = 10

k*x^2 = (3*b - a)*x^2

k = (3*b - 10)  

0*x = (3*c - b)*x

0 = (3*c - b)

b = 3*c

and

1 = -c

then:

c = -1

Replacing this in the equation: b = 3*c

we get: b = -3

Replacing this in the equation for k, we get:

k = (3*b - 10) = (3*-3 - 10) = -19

k = -19

And we can write:

P(x) = (3*x - 1)*(10*x^2 - 3*x - 1)

b) Now we want to write P(x) as a product of its linear factors.

Then we need to factorize the quadratic part:

We need to solve

10*x^2 - 3*x - 1 = 0

We can use the Bhaskara's equation to get the solutions:

[tex]x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*10*(-1)} }{2*10} = \frac{3 \pm 7}{10}[/tex]

Then the two zeros of that polynomial are

x = (3 + 7)/10 = 1

x = (3 - 7)/10 = - 4/10 = -2/5

So we can write the polynomial as:

10*(x - 1)*(x - (-2/5))

Replacing this in the equation of P(x) we get:

P(x) = (3*x - 1)*10*(x -1)*(x + 2/5)

     = 10* (3*x - 1)*(x -1)*(x + 2/5)

So P(x) is written as a product of lineal factors.

C) The zeros of the polynomial are the values of x such that one of the factors becomes equal to zero.

For the first factor, we have a zero at x = 1/3

for the second, we have a zero at x = 1

for the third one, we have a zero at  x = -2/5

Answer:

255

Step-by-step explanation:

Once split up you find the are of the rectangle which is 8*17=136

Then since the bottom line is 22, you do 22-8 to find the bottom line of the triangle.

The area of the triangle is 17*14/2=238/2

Hence, 119

Hope it helps!

Answer:

63

Step-by-step explanation:

I hope

Answer:

Use distance formula to find the length of the segments

1. H = (-3, 0), F = (3, 2)

2. E = (1, 4), G = (-1, -2)

3. We see the diagonals are congruent, opposite sides are parallel.

The above is the property of a rectangle

Answer:

x = 61°

Step-by-step explanation:

since the triangle is isosceles the two angles opposite 58° are equal so:

x = (180° - 58°)/2 = 61°

Answer:

I think too that many different will be there in case such things ..

Answer: el último

Step-by-step explanation:

Answer:

He is incorrect

Step-by-step explanation:

Given

3(x + 1) - 5 = 3x - 2 ← simplify left side

3x + 3 - 5 = 3x - 2

3x - 2 = 3x - 2

Since both sides are equal, then this indicates that the equation has infinite solutions.

Answer:

Matter in living things may pass into nonliving things.

Step-by-step explanation:

Answer:

y=9

Step-by-step explanation:

4-2y+8=-6

-2y=-4-8-6

-2y=-18 divide by -2 both side

y=-18/-2

y=9

Answer:

D

Step-by-step explanation:

40% = [tex]\frac{40}{100}[/tex] = [tex]\frac{2}{5}[/tex] ← in simplest form

Then

[tex]\frac{2}{5}[/tex] of $120 = [tex]\frac{2}{5}[/tex] × $120 = 2 × $24 = $48

she pays $120 - $48 = $72

Answer:

I am going to assume that D's expression is actually $2.99+$3.19+$2.59+(-$0.25)+(-$0.40)

= $6.18+$2.59-$0.25-$0.40 [Note: (+)*(-)=(-)]

=$8.77-$0.25-$0.40

=$8.52-$0.40

=$8.12

Step-by-step explanation:

The prices of the loaf bread, a jar of peanut butter and 3 pounds of apples will be added. The value of the coupons will be then reduced from the total to get the final total.

Answer:

3960

Step-by-step explanation:

i dont know

my sister helped me hope i get it right

Answer:

photography

Step-by-step explanation:

Answer:

i believe it is 70

Step-by-step explanation:

6×12=72

6-4=2

72-2=70

Step-by-step explanation:

blue: 4x+2+7x+7+5x -4 = 16x +5

red: x+3+x+7+2x-5 = 4x -5

difference: 16x+5 - (4x -5) = 12x +10

Answer:

The answer is 33 years.

Step-by-step explanation:

10% of 3 is .3

Just move the decimal to the left.

.3 times 33=9.9

9.9~10

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

just took the test

Answer:

10

Step-by-step explanation:

5*2=10

2+2+2+2+2=10

Answer:

The midpoint is (-2,14) and the slope is m=1/3

Step-by-step explanation:

Answer:

24 im pretty sure.

Step-by-step explanation:

Answer:

r = 7.3 m

Step-by-step explanation:

A = (pi)(radius)^2, so, if A = 167 m^2, r^2 is found as follows:

         167 m^2

r^2 = -------------- = 53.158 m^2

              3.14

Taking the square root of both sides, we get

r = 7.3 m

This is correct, because A = (pi)(radius)^2 becomes (3.14)(7.3 m)^2 = 167.4 m^2

Answer:

31%

33%

Step-by-step explanation:

I'm not 100% sure. I tried my best.

Answer:

1: 9

2: i dont know sorry

3: 21/2

Step-by-step explanation:

1: know that the bottom portion of the triangle is 18  the bottom left is 12 and the top left is 6. Now you could say that its six because they look the same size but we cant be sure, and six isnt an option. i dont know how to solve so we're using process of elimination so bare with me. we alread have 12 and 18 and theyre way bigger, it cant be 11 because it wouldnt be that small. so in my mind its 9.  

2:  n/A

3: because i said so

Answer:

#1

Option D

#2

#3

Option B

Answer:

Step-by-step explanation:

This is the sum of the first 4 terms, substitute n for each term:

4

∑   [tex]\frac{7}{n}[/tex] = 7/1 + 7/2 + 7/3 + 7/4

n=1

Correct choice is A

[tex] \displaystyle \sum^{4} _{n = 1} \: \frac{7}{n} = \: 7 + \frac{7}{2} + \frac{7}{3} + \frac{7}{4} [/tex]