find all positive integral values of k for which the given trinomial can be factored

Question

1 . x² + kx + 21 =

2 . a² + ka + 72 =

3 . c² + kc + 45 =

4 . d² + kd - 28 =

5 . n² + 10n + k =

6 . g² + kg - 36 =

7 . q² - kq - 27 =

8 . t² - kt - 48 =

9 . u² - ku - 28 =

Answer 1

1 x^2 + 11x + 21 = x+7 x+3

x^2 -11x +21 = x-7 x-3

x^2 +22x +21 = x+21 x+1

x^2 -22x + 21 = x-21 x-1

21=21x1,

-21x-1,

7x3,

-7x-3

2 a^2 + 73a + 72 = a+72 x a+1

a^2 -73a + 72 = a-72x a-1

72=3x3x2x2x2 has

72, 1, + - 73

32, 2, +- 38

16, 4 +- 20

12,6, +- 18

9, 8 + - 17

+ - 73a, 38a, 20a, 18a, 17a

3 45= 3x3x5

+ - 46c, 18c, 14c,

4 see #9

5 n^2 +10n + 9

6 -36 = -36x1, 36x-1 -- -35, +35

= -18x2 18x-2 -- -16, +16

= -12x3 12x-3 -- -9 + 9

= -9x4 9x-4 --- -5 +5

= -6x6 -- -6 +6

7 -27 = -27x1 27x-1 -- -26, +26

-27 = -9 x3 9x-3 -- -6, +6

8 -48 = -48x1, 48x-1 --- -47 +47

-48 = -24x2 24x-2 -- -22, +22

-48 = -16x3, 16x-3 --- -13, +13

-48 = -12x4, 12x-4 --- -8, +8

-48 = -8 x 6, 8x-6 ---- -2, +2

9 u^2 -271u - 28 = (u-28)(u+1)

u^2 +11u - 28 = (v+28)(v-1)

v^2 +12v - 28 = v+14 v-2

v^2 -12v +28 = v-14 v+2

v^2 +4v - 28 = v+7 v-4

v^2 -4v - 28 = v-7 v+4