Answer:
a) (x +7)(x -2)
b) x = -7 or +2
Step-by-step explanation:
a)
A trinomial is factored by realizing that the constant term (-14) is the product of the binomial constants, and the coefficient of the linear term (5) is their sum. Here, we can examine the factorization of -14 to see which factors may have a sum of 5:
-14 = (-1)(14) = (-2)(7) = (-7)(2) = (-14)(1)
Sums of these factor pairs are 13, 5, -5, -13. Clearly, we could stop writing factorizations when the sum stops being positive. The values of interest are -7 and 2. They tell us the trinomial is factored as ...
x² +5x -14 = (x +7)(x -2)
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b)
The zeros of the quadratic are the values of x that make the above factors be zero. The zero product rule tells you the only way the product will be zero is for a factor to be zero.
x +7 = 0 ⇒ x = -7
x -2 = 0 ⇒ x = 2
The solutions are x = -7 or x = 2.
