Factor each expression. 17. 5x2 - 17x + 6 18. 3x2 + 10x + 8 19. 2b2 - 9b - 5 20. Z2 + 12z + 36 21. 9x2 - 6x + 1 22. 4k2 + 12k + 9 23. N2 - 49 24. 2x2 - 50

Step-by-step explanation:

17. 5x² - 17x+6 = 0

the coefficient of 5x² is 5, we multiply it by 6 which is 30

then we look for two numbers we can multiply together to give + 30 and add together to give - 17x

the possible number is - 15, - 2

5x² - 17x+6 = 0

(5x² - 15x) - (2x+6) = 0

5x (x-3) - 2 (x-3) = 0

(5x-2) (x-3) = 0

5x-2 = 0 x-3 = 0

5x = 2 x = 3

x=2/5

x = 2/5, 3

18. 3x²+10x+8

3x²+6x+4x+8

3x (x+2) + 4 (x+2)

(3x+4) (x+2) = 0

3x+4 = 0 x+2 = 0

3x = - 4 x=-2

x=-4/3, - 2

x = - 4/3, - 2

19. 2b² - 9b - 5

(2b² + 1b) - (10b - 5)

b (2b+1) - 5 (2b+1) = 0

(b-5) (2b+1) = 0

b-5=0 2b+1=0

b=5 2b=-1

b=5 b = - 1/2

b = 5, - 1/2

20. z² + 12z + 36

z² + 6z + 6z + 36

z (z+6) + 6 (z+6)

(z+6) (z+6) = 0

z+6=0 z+6=0

z = - 6 z = - 6

z = - 6

21. 9x² - 6x + 1

9x² - 3x - 3x + 1

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

(3x-1) (x-1) = 0

3x-1=0 x-1=0

3x=1 x=1

x=1/3

x=1, 1/3

22. 4k² + 12k + 9

4k² + 6k + 6k + 9

2k (2k+3) + 3 (2k+3)

(2k+3) (2k+3)

2k+3 = 0

2k = - 3

k = - 3/2

23. n² - 49 = 0

n² = 49

n = √49 = 7

24. 2x² - 50 = 0

2x² = 50

x² = 50/2 = 25

x² = 25

x = √25 = 5