Question

9. Consider the function f(x) = x² + 3x – 4.

Part A: What is the factored form of f(x)? Show
your work.
a.f(x) = (x + 1)(x – 4)
b.f(x) = (x - 1)(x + 3)
c.f(x) = (x + 4)(x - 1)
d.f(x) = (x − 2)(x + 2)

Answer 1

c. f(x) = (x + 4)(x - 1)

Explanation:

Since you're familiar with the product of two binomials:

(x +a)(x +b) = x² + (a+b)x + ab

you know that the constants in the binomial factors must ...

• have a product of -4
• have a sum of +3

__

All of the choices except B have binomial constants that have a product of -4.

In order, the sums of the remaining choices are ...

A: 1-4 = -3

C: 4-1 = 3 . . . . this is the correct choice

D: -2+2 = 0