Question

Which values could replace C to make x^2 +7x+c factorable

Answer 1

Explanation:

hello : in R

x² +7x+c factorable when : ∆ ≥ 0

∆= b²-4ac a= 1 and b=7 c =?

∆= 7²-4(1)(c)

49- 4c ≥ 0

49≥ 4c

4c ≤ 49

values could replace C are :

c ≤ 49/4

Answer 2

0, 6, 10, 12

Explanation:

`(x+a)(x+b)=x^2+(a+b)x+ab\\a+b=7\\ab=c`

We can now find potential values for c, knowing what our constraints are.

`c=0,b=7,c=0\\a=1,b=6,c=6\\a=2,b=5,c=10\\a=3,b=4,c=12\\a=4,b=3,c=12\\a=5,b=2,c=10\\a=6,b=1,c=6\\a=7,b=0,c=0`

We can say that c being 0 is the trivial solution as your expression becomes:

`x^2+7x+0`

which can be factorised to

`x(x+7)`