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Sloan [31]
2 years ago
11

On a test, leo is asked to completely factor the polynomial 3x3 – 3x 5x2 – 5. he uses double grouping to get (x2 – 1)(3x 5). has

he factored the polynomial completely? explain.
Mathematics
2 answers:
Agata [3.3K]2 years ago
8 0

No, Leo's answer is not a product of prime polynomials because x2 – 1 can be factored. This is a difference of squares. He should continue factoring to get

(x – 1)(x + 1)(3x + 5).

____ [38]2 years ago
7 0

Answer:

Leo does not  factored the polynomial completely.

3x^3-3x+5x^2-5=(x+1)(x-1)(3x+5)

Step-by-step explanation:

Given: On a test, Leo is asked to completely factor the polynomial 3x^3-3x+5x^2-5.

also, he uses double grouping to get(x^2- 1)(3x+5)

We have to explain whether he  factored the polynomial completely or not.

Consider the given polynomial 3x^3-3x+5x^2-5.

after double grouping he get (x^2- 1)(3x+5)

Also, we can simplify further ,

Using algebraic identity a^2-b^2=(a+b)(a-b)

We get,

(x^2- 1)=(x+1)(x-1)

We get, (x^2- 1)(3x+5)=(x+1)(x-1)(3x+5)

Thus, 3x^3-3x+5x^2-5=(x+1)(x-1)(3x+5)

Thus, He does not  factored the polynomial completely.

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Given TS¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ are midsegments, PR=18.2, TS=6.5. Find QU . A. 9.1 B. 3.25 C. 13 D. 6.5
AleksAgata [21]

Answer:

The correct option is;

D. 6,5

Step-by-step explanation:

TS and TU are midsegments

Segment PR = 18.2

Segment TS = 6.5

Given that TS is the midsegment of PR and PQ, therefore, TS = 1/2×QR

Which gives;

Segment QR = 2×TS = 2 × 6.5 = 13

Segment QR = 13

Given that TU is a midsegment to PQ and QR, we have that QU = UR

Segment QR = QU + UR (segment addition postulate)

Therefore, QR = QU + QU (substitute property of equality)

Which gives;

QR = 2×QU

13 = 2×QU

Segment QU = 13/2 = 6.5

The length of segment QU is 6.5.

5 0
2 years ago
which of the statements about the following quadratic equation is true? 6x2 - 8 = 4x2 7x the discriminant is greater than zero,
d1i1m1o1n [39]
6x^2 - 8 = 4x^2 + 7x
6x^2 - 4x^2 - 7x - 8 = 0
2x^2 - 7x - 8 = 0
discriminant = b^2 - 4ac; where a = 2, b = -7 and c = -8
d = (-7)^2 - 4(2)(-8)
d = 49 + 64
d = 113

the discriminant is greater than zero, so there are two real roots


5 0
2 years ago
Read 2 more answers
Jesus wants to start saving for college. His parents started an account for him that currently holds $325. Jesus adds $50 each m
erma4kov [3.2K]

Answer:

y-intercept, c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

Step-by-step explanation:

We are given the following in the question:

A saving account currently holds $325. Jesus adds $50 each month.

Let x be the number of months and y be the total money n the saving account.

Then, we can use a linear function to represent the money in the account.

y(x) = 325 + 50x

Comparing to general linear function,

y = mx + c

where m is the slope and tells the rate of change and c is the y-intercept that is the value when x is zero.

Comparing we get:

m = 50

c = 325

y-intercept = c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

The attached image shows a graph for the same.

7 0
2 years ago
A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored f
AnnZ [28]
Volume of cube=side³
ok, so you need to know the difference or sum of cubes
a³+b³=(a+b)(x²-xy+y²)
so

(4p)³+(2q²)³=
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(4p+2q²)(16p²-8pq²+4q⁴)

3rd option
5 0
2 years ago
You are at the bottom of a mountain where the temperature is 74°F. The top of the mountain is 5500 feet above you. What is the t
mamaluj [8]

For every 1,000 feet you go up in elevation, the temperature decreases by about 3.3°F

 

Given:

Temperature at the bottom of the mountain is 74°F

The top of the mountain is 5500 feet above you

 

Change (reduction) in temperature is 3.3 X 5500 / 1000

= 18.15°F

 

Temperature at the top of the mountain is 74°F – 18.15°F

= 55.85°F

3 0
2 years ago
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