Math Help??? Polynomials???

Question

1) Factor the following polynomial completely.
4 x^2 - 27 x + 35

2) Factor the following polynomial completely.
8 x^2 - 50 x - 13

3) Factor the following polynomial completely.
9 x^2 - 1

4) Factor the following polynomial completely.
27 x^2 - 363

Any help would be greatly appreciated! Thank you!

Answer 1

[14]
4x^2-27x+35
=4x^2-20x-7x+35
=4x(x-5)-7(x-5)
=(x-5)(4x-7)
(2) 8x^2-50x-13
=8x^2+2x-52x-13
=2x(4x+1)-13(4x+1)
=(4x+1)(2x-13)
(3)9x^2-1
=(3x)^2-(1)^2
=(3x+1)(3x-1)
(4)27x^2-363
=3(9x^2-121)
=3{(3x)^2-(11)^2}
=3(3x+11)(3x-11)

Answer 2

For these problems, we basically use the trial and error method,
that is taking the factors of the first and last numerical coefficients or simply the first and last numbers without the variables

in the case of number 1, (as an example) we basically get the
factors of 4 and 35

for 4 we have 4 and 1 and for 35 we have 7 and 5
arranging:

4 7

1 5

there is a basic principle that if you cross multiply these numbers and add them, you would get the middle term...

in our case we need to get -27 in order to get that, we need to replace our factors with -7 and -5 since (-7)X(-5) is still +35

so cross multiplying we get -20 and -7

and thus -27

its factos would then be

4x - 7

x - 5

just remember, if the factors you get doesnt work, use other factors.
No. 1

(4x-7)(x-5)

No. 2

(4x+1)(2x-13)

No. 3

Difference of two squares:
(3x-1)(3x+1)

No. 4

(9x-33)(3x+11)

Answer 3

1. 4x² - 27x + 35 = (4x - 7)(x - 5)
2. 8x² - 50x - 13 = (4x + 1)(2x - 13)
3. 9x² - 1 = (3x + 1)(3x - 1)
4. 27x² - 363 = 3(9x² - 121) = 3(3x + 11)(3x - 11)

Answer 4

1. (4x-7)(1x-5)
2. (4x+1)(2x-13)
3. (3x+1)(3x-1)

(:

and I'm not sure about 4.. and I have no paper to try and work it out on, sorry! but I hope this helps.

Answer 5

1) (4x - 7)(x - 5)

2) (4x + 1)(2x - 13)

3) (3x - 1)(3x + 1)

4) 3(3x - 11)(3x +11)

good luck

Answer 6

3) (3x^2-1)(3x^2 +1)
1) (4x-7)(x-5)