Question

Given f(x)=2x3−5x2−68x+35
, apply the Factor Theorem and determine which of the following is a factor of f(x)
.(1 point)
Responses

(x+5)
left parenthesis x plus 5 right parenthesis

(x−3)
left parenthesis x minus 3 right parenthesis

(2x+1)
left parenthesis 2 x plus 1 right parenthesis

(x+7)

Answer 1

To determine which of the given factors is a factor of f(x), we need to check if f(x) is equal to zero when we plug in the value of that factor.

1. Let's check if f(x) is equal to zero when x = -5:
f(-5) = 2(-5)^3 - 5(-5)^2 - 68(-5) + 35
= 2(-125) - 5(25) + 340 + 35
= -250 - 125 + 340 + 35
= 0

Since f(-5) is equal to zero, (x+5) is a factor of f(x).

2. Let's check if f(x) is equal to zero when x = 3:
f(3) = 2(3)^3 - 5(3)^2 - 68(3) + 35
= 2(27) - 5(9) - 204 + 35
= 54 - 45 - 204 + 35
= -160

Since f(3) is not equal to zero, (x-3) is not a factor of f(x).

3. Let's check if f(x) is equal to zero when x = -1/2:
f(-1/2) = 2(-1/2)^3 - 5(-1/2)^2 - 68(-1/2) + 35
= 2(-1/8) - 5(1/4) + 34 + 35
= -1/4 - 5/4 + 34 + 35
= 68 - 6
= 62

Since f(-1/2) is not equal to zero, (2x+1) is not a factor of f(x).

4. Let's check if f(x) is equal to zero when x = -7:
f(-7) = 2(-7)^3 - 5(-7)^2 - 68(-7) + 35
= 2(-343) - 5(49) + 476 + 35
= -686 - 245 + 476 + 35
= -420 + 511
= 91

Since f(-7) is not equal to zero, (x+7) is not a factor of f(x).

Therefore, the only factor of f(x) among the given options is (x+5).