When 𝑥3 − 2𝑥2 + 𝑚𝑥 + 4 is divided by 𝑥 − 3, the remainder is −2, find ma. −2b. −5c. −3d. −4
Question
When is divided by , the remainder is -2, find
- a. -2
- b. -5
- c. -3
- d. -4
Solution
To solve this problem, we can use the Remainder Theorem which states that if a polynomial f(x) is divided by (x-a), the remainder is f(a).
Given that when the polynomial x³ - 2x² + mx + 4 is divided by (x - 3), the remainder is -2, we can substitute x = 3 into the polynomial and set it equal to -2.
So, we have:
3³ - 2(3²) + 3m + 4 = -2 27 - 18 + 3m + 4 = -2 13 + 3m = -2 3m = -2 - 13 3m = -15 m = -15 / 3 m = -5
So, the correct answer is b. -5.
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