Answer:
A) x = {5, 7}
B) The solutions make the equation true.
Step-by-step explanation:
Part A:
To solve this by factoring, you need to find factors of 35 that have a sum of -12. Since 35 is the product of two primes, the search is a short one.
35 = (-1)(-35) = (-5)(-7)
The corresponding sums are -36 and -12, so the latter factor pair is the one we want. Since the coefficient of x^2 is 1, we can use these numbers directly in the binomial factors:
x^2 -12x +35 = (x -5)(x -7) = 0
The zero product rule tells us this product is zero only when one of the factors is zero:
x -5 = 0 ⇒ x = 5
x -7 = 0 ⇒ x = 7
The two solutions are x=5 and x=7.
__
Part B:
The solutions from part A are the x-intercepts of the graph of the quadratic expression. They are the values of x that make the quadratic expression be zero. That is, they are the values of x that make the equation true.
