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KengaRu [80]
3 years ago
10

How to factor this polynomial? And solve

Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
7 0
12x^3 - 14x^2 - 6x

GCF is 2x:-

= 2x(6x^2 - 7x - 3)

= 2x [ 6x^2 + 2x - 9x - 3]

=  2x [2x(3x + 1) - 3(3x + 1)]

= 2x(2x - 3)(3x + 1)  Answer
You might be interested in
19. A carpenter is putting a skylight in the roof. If the roof measures (10x + 9) by (7x + 7) and the skylight measures (x + 5)
velikii [3]
19)  67x²+115x+48
20) (w+8)²
21) (d+11)²
22) (r+7)(r-7)

Explanation:
19)  The area of the ceiling is given by (10x+9)(7x+7).  Multiplying we have:
10x*7x+7*10x+9*7x+9*7
=70x²+70x+63x+63
=70x²+133x+63

The area of the skylight is given by (x+5)(3x+3).  Multiplying we have:
x*3x+3*x+5*3x+5*3
=3x²+3x+15x+15
=3x²+18x+15

To find the remaining area of the ceiling we subtract:
(70x²+133x+63)-(3x²+18x+15)
=70x²+133x+63-3x²-18x-15
=67x²+115x+48

20)  To factor, we want to find factors of c, 64, that sum to b, 16.  8*8=64 and 8+8=16; therefore we have:
(w+8)(w+8)
Since this is the same binomial twice, we write it as (w+8)²

21)  Again we look for factors of c, 121, that sum to b, 22.  11*11=121 and 11+11=22, so:
(d+11)(d+11)
Since this is the same binomial twice, we have (d+11)²

22)  Factors of -49 that sum to 0 (there is no r term, just r²):  -7*7=-49 and -7+7=0, so:
(r-7)(r+7)
6 0
3 years ago
Integration using part formula<br> <img src="https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5Enlogx%7D%20%5C%2C%20dx" id="TexFor
liq [111]

Answer:

Integration of I= \int {x^{n}logx \, dx=[\frac{logx}{n+1} x^{(n+1)}]-[\frac{1}{(n+1)^{2}}x^{(n+1)}]

Step-by-step explanation:

Given integral is I= \int {x^{n}logx \, dx

Take logx=t

x=e^{t}

x^{n}=e^{nt}

\frac{1}{x} dx=dt

dx=xdt

dx=e^{t}dt

I= \int (e^{nt})(t)(e^{t})\, dt

I= \int (e^{(n+1)t})(t)\, dt

Using integration by part,

I= (t)\int [e^{(n+1)t}]\, dt-\int[\frac{d}{dt}{t}\times\int (e^{(n+1)t})]\\\\I= (t) [\frac{1}{n+1}e^{(n+1)t}]-\int[1\times\frac{1}{n+1}e^{(n+1)t}]\,dt\\\\I=[\frac{t}{n+1}e^{(n+1)t}]-[\frac{1}{(n+1)^{2}}e^{(n+1)t}]

Writing in terms of x

I=[\frac{t}{n+1}e^{(n+1)t}]-[\frac{1}{(n+1)^{2}}e^{(n+1)t}]

I=[\frac{logx}{n+1}e^{(n+1)logx}]-[\frac{1}{(n+1)^{2}}e^{(n+1)logx}]

I=[\frac{logx}{n+1}e^{logx^{(n+1)}}]-[\frac{1}{(n+1)^{2}}e^{logx^{(n+1)}}]

I=[\frac{logx}{n+1} x^{(n+1)}]-[\frac{1}{(n+1)^{2}}x^{(n+1)}]

Thus,

Integration of I= \int {x^{n}logx \, dx=[\frac{logx}{n+1} x^{(n+1)}]-[\frac{1}{(n+1)^{2}}x^{(n+1)}]

3 0
3 years ago
A line passes through (2,4) and (-2,2).
Diano4ka-milaya [45]

Answer:

a) (6;6)

b) Yes

d) The intersection is on the vertical axis.

Step-by-step explanation:

a) A(2,4)

B (2,2)

Vecto BA (4, 2)

Vecto n (-4,2)

We have:

(2 - 4) x (X - (-2)) + (2 - (-2)) x (Y - 2) = 0

=> -2X + 4Y - 12 = 0

=> Y = X/2 +3

Let's find the value of y if (6,y) lies on the  plane:

Put X = 6 => Y = 6

b)

X/2 + 3 = 3 - X

=> X/2 = -X

=> X =0 -> Y = 3

C (0;3)

d) The intersection is on the vertical axis.

I hope my answer will help you.

7 0
3 years ago
Simplify x^2-4x+4/x^2-4
MatroZZZ [7]

Answer:

x2 - 4x - 4

 ———————————

    x - 2  

Step-by-step explanation:

4 0
3 years ago
Is ten a perfect square
Contact [7]
Answer:
 No, it is not a perfect square.
7 0
3 years ago
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