Answer: (b) x = -7, x = 2, x = 4
<u>Step-by-step explanation:</u>
Remainder Theorem is used to determine if a given value is a root.
It is stated that (x + 7) is a root ⇒ x + 7 = 0 ⇒ x = -7
We can confirm this by plugging in x = -7 and getting a value of 0.
f(x) = 5x³ + 5x² - 170x + 280
f(-7) = 5(-7)³ + 5(-7)² - 170(-7) + 280
= -1715 + 245 + 1190 + 280
= 0
CONFIRMED that x = -7 is a zero!
Next, let's try x = 2
f(2) = 5(2)³ + 5(2)² - 170(2) + 280
= 40 + 20 - 340 + 280
= 0
CONFIRMED that x = 2 is a zero!
Lastly, let's try x = 4
f(4) = 5(4)³ + 5(4)² - 170(4) + 280
= 320 + 80 - 680 + 280
= 0
CONFIRMED that x = 4 is a zero!
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