Question

#2: review
a factor of $2.5x^2 - 30x + c$ is $x + 4$. what is the value of $c$
a. $-160$
b. $-26$
c. $80$
d. $110$

Explanation:

Step1: Find root from factor

If $x+4$ is a factor, then $x = -4$ is a root.

Step2: Substitute root into polynomial

Substitute $x=-4$ into $2.5x^2 - 30x + c = 0$:
$$2.5(-4)^2 - 30(-4) + c = 0$$

Step3: Calculate each term

Compute the squared and linear terms:
$$2.5(16) + 120 + c = 0$$
$$40 + 120 + c = 0$$

Step4: Solve for c

Combine constants and isolate $c$:
$$160 + c = 0$$
$$c = -160$$

Answer:

A. $-160$