Answer:
(x+5)(x+7)
Step-by-step explanation:
We need to find two binomials of the form (x+a) and (x+b) such that their product gives [tex]x^2+12x+35[/tex]
So, notice that the values for "a" and for "b" in the binomials to factor should verify that :
1) a * b = 35
and 2) a+b = 12
Since the product (x+a) times (x+b) = [tex]x^2+ax+bx+a*b= x^2+(a+b)x +a*b[/tex]
The pair of values 7 and 5 satisfy such conditions.
Therefore (x+5) (x+7) = [tex]x^2+12x+35[/tex]
and then (x+5) and (x+7) are binomial factors of the original trinomial.
