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Georgia [21]
3 years ago
7

Is the binomial a factor of the polynomial function?

Mathematics
1 answer:
olchik [2.2K]3 years ago
7 0

Answer:

YES

NO

NO

Step-by-step explanation:

The given polynomial is: $ f(x) =  x^3 + 4x^2 - 25x - 100 $

(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.

To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.

∴ f(5) = 5³ + 4(5)² - 25(5) - 100

        = 125 + 100 - 125 - 100

        = 225 - 225

        = 0

We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.

Now, to check (x + 2) is a factor.

i.e., to check x = - 2 satisfies f(x) or not.

f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100

      = -8 + 16 + 50 - 100

     = -108 + 66

     ≠ 0

Therefore, (x  + 2) is not a factor of f(x).

To check (x - 4) is a factor.

∴ f(4) = 4³ + 4(4)² - 25(4) - 100

        = 64 + 64 - 100 - 100

        = 128 - 200

        ≠ 0

Therefore, (x - 4) is not a factor of f(x).

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jekas [21]
The answer is 4.

The reason is that 5 times 4 is 20.
7 0
2 years ago
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1.48 as a fraction ​
Leni [432]

Answer:

148/100=37/25

Step-by-step explanation:

Who have to think how many zeros it took for the decimal to get between the 1 and 4.

148/100=37/25 is your answer.

4 0
3 years ago
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Chin canned a number of quart jars anf a number of pints jars of tomatoes from hid garden. A pint is 16 onces and a quart is 32
ryzh [129]

Answer:

The equation which models the scenario is:   16 p + 32 q  = 1280

Step-by-step explanation:

The total number of pints packed  = p

The total number of quarts  packed  = q

The weight of 1 pint jar of tomatoes  = 16 oz

So, the total weight of p pints  = p x ( Weight of 1 pint) = p x ( 16 oz) = 16 p

The weight of 1 quart jar of tomatoes  = 32 oz

So, the total weight of q quarts  = q x ( Weight of 1 quart) = q x ( 32 oz)

= 32 q

Now, the TOTAL WEIGHT of p pints and q quarts

= Total weight of { p pints +  q quarts}  = 16 p + 32 q

Also, chin canned a total of 1280 ounces.

⇒ TOTAL WEIGHT of p pints and q quarts = 1280 ounces

or,   16 p + 32 q  = 1280 ounces

Hence, equation which models the scenario is:   16 p + 32 q  = 1280

8 0
3 years ago
Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence
pentagon [3]

Answer:  A.   A=(1000-2w)*w      B. 250 feet

C.  125 000 square feet

Step-by-step explanation:

The area of rectangular is A=l*w    (1)

From another hand the length of the fence is 2*w+l=1000        (2)

L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.

Express l from (2):

l=1000-2w

Substitude l in (1) by 1000-2w

A=(1000-2w)*w        (3)   ( Part A. is done !)

Part B.

To find the width w  (Wmax) that corresponds to max of area A   we have to dind the roots of equation (1000-2w)w=0  ( we get it from (3))

w1=0  1000-2*w2=0

w2=500

Wmax= (w1+w2)/2=(0+500)/2=250 feet

The width that maximize area A is Wmax=250 feet

Part C.   Using (3) and the value of Wmax=250 we can write the following:

A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets

3 0
3 years ago
3 An open cone has a vertical angle measuring 40°
belka [17]

Answer:

13.41 cm

Step-by-step explanation:

The radius, height, and HALF of vertical angle makes a triangle.

Where

Radius will be the base of the triangle

Height will be the "height" of the triangle

Top angle will be HALF of vertical angle (40/2 = 20)

From the 20 degree angle, the side "opposite" would be the radius, which is 30. The side "adjacent" would be the height, let it be h.

<em>Which trig ratio relates opposite and adjacent? Yes, that is TAN. Thus we can write:</em>

Tan(20) = opposite/adjacent

Tan(20) = 30/h

h = 30/Tan(20)

h = 13.41

So

The height of the cone would be around 13.41 cm

3 0
3 years ago
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