Question

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

Answer 1

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