Question

1. ( x^2 + 10x + 60 = 0 )
2. ( x^2 + 25x + 100 = 0 )
3. ( x^2 + 19x + 84 = 0 )
4. ( x^2 + 22x + 120 = 0 )

Explanation:

Step1: Factor quadratic 2

Find two numbers: product=60, sum=16: 6 & 10
$x^2+16x+60=(x+6)(x+10)=0$

Step2: Solve for x (Q2)

Set each factor to 0:
$x+6=0 \implies x=-6$; $x+10=0 \implies x=-10$

Step3: Factor quadratic 3

Find two numbers: product=100, sum=25: 5 & 20
$x^2+25x+100=(x+5)(x+20)=0$

Step4: Solve for x (Q3)

Set each factor to 0:
$x+5=0 \implies x=-5$; $x+20=0 \implies x=-20$

Step5: Factor quadratic 4

Find two numbers: product=84, sum=19: 7 & 12
$x^2+19x+84=(x+7)(x+12)=0$

Step6: Solve for x (Q4)

Set each factor to 0:
$x+7=0 \implies x=-7$; $x+12=0 \implies x=-12$

Step7: Factor quadratic 5

Find two numbers: product=120, sum=22: 10 & 12
$x^2+22x+120=(x+10)(x+12)=0$

Step8: Solve for x (Q5)

Set each factor to 0:
$x+10=0 \implies x=-10$; $x+12=0 \implies x=-12$

Answer:

1. $x = -6$ or $x = -10$
2. $x = -5$ or $x = -20$
3. $x = -7$ or $x = -12$
4. $x = -10$ or $x = -12$

Factor Tables:

For Question 2:

FACTOR 1	1	2	3	4	5	6

For Question 3:

FACTOR 1	1	2	4	5	10	20

For Question 4:

FACTOR 1	1	2	3	4	6	7

For Question 5:

FACTOR 1	1	2	3	4	5	6	8	10