Use Remainder theorem to factorize the following polynomial

Use Remainder theorem to factorize the following polynomial

2𝑥³ + 3𝑥² - 9𝑥 - 10

Answer

f(𝑥) = 2𝑥³ + 3𝑥² - 9𝑥 - 10
2𝑥³ + 3𝑥² - 9𝑥 - 10
= 2 × 2³ + 3 × 2² - 9 × 2 - 10                (Putting x = 2)
= 16 + 12 - 10 - 10
= 0 ∴ (x – 2) is a factor
2𝑥³ + 3𝑥² - 9𝑥 - 10 = (𝑥 - 2)(2𝑥² + 7𝑥 + 5)
= (𝑥 - 2)(2𝑥 + 5)(𝑥 - 2)

• Exam Year: 2018