Question

if x²-4x+c is exactly divisible by (x-1) then c is... ​

Answer 1

Answer:

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Answer 2

If x² - 4x + c is exactly divisible by (x - 1), it means the remainder after division will be 0.

✰ Using remainder theorem,

x - 1 = 0

⇒x = 1

Substitute x = 1 in x² - 4x + c

p(x) = x² - 4x + c = 0

p(1) = 1² - 4(1) + c = 0

⇒ p(1) = 1 - 4 + c = 0

⇒ p(1) = -3 + c = 0

-3 + c = 0

✰ c = 3

☞ Additional information:

• The remainder theorem states that if any polynomial f(x) is divided by polynomial x - a, remainder is equal to the value of f(a).
• Factor theorem states that if 'a' is a zero of polynomial f(x), then x - a is factor of f(x) and vice versa