Factor the trinomial:
5x^2+41x+42

(5x + 6) (x + 7)

Step By Step Explanation:

Use the sum form to the product.

5

(5x+6)(x+7)

Step-by-step explanation:

Factor the expression by grouping. Expression needs to be rewritten as 5x  

2 +ax+bx+42.

To find a and b

a+b=41

ab=5×42=210

Since ab is positive, a and b have the same sign.  List all such integer pairs that give product 210.

1,210

2,105

3,70

5,42

6,35

7,30

10,21

14,15

Calculate the sum for each pair.

1+210=211

2+105=107

3+70=73

5+42=47

6+35=41

7+30=37

10+21=31

14+15=29

The solution is the pair that gives sum 41.

a=6

b=35

Rewrite 5x  

2 +41x+42 as (5x^2 +6x)+(35x+42).

Factor out x in the first and 7 in the second group.

x(5x+6)+7(5x+6)

Factor out common term 5x+6 by using distributive property.

(5x+6)(x+7)

the answer

b. they are parallel and will never intersect.