Question

Factor the following equation to find its zeros.

Answer 1

Answer:

  A|  12, 3

Step-by-step explanation:

The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...

  y = (x -12)(x -3)

A quick check shows this product is ...

  y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required

The factors are zero when x is either 12 or 3.

The zeros of the equation are 12 and 3.

____

Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).

Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.