Question

If the remainder obtained on dividing the polynomial 2x³ − 9x² + 8x + 15 by (x − 1) is R₁ and the remainder obtained on dividing the polynomial x² − 10x + 50 by (x − 5) is R₂, then what is the value of R₁ − R₂?

• A. -9
• B. -5
• C. 5
• D. 9

Answer 1

The correct option is A

-9

According to the remainder theorem, when a polynomial p(x) is divided by a linear polynomial (x − a), the remainder obtained is p(a).

Let f(x) = 2x³ − 9x² + 8x + 15 and g (x) = x² − 10x + 50

Now, the zero of (x − 1) is 1.

It is given that the remainder obtained on dividing the polynomial f(x) by (x − 1) is R₁.

∴ R₁ = f(1)

⇒ R₁ = 2(1)³ − 9(1)² + 8(1) + 15 = 2 − 9 + 8 + 15 = 25 − 9 = 16

The zero of (x − 5) is 5.

It is given that the remainder obtained on dividing the polynomial g(x) by (x − 5) is R₂.

∴ R₂ = g(5)

⇒ R₂ = (5)² − 10(5) + 50 = 25 − 50 + 50 = 25

∴ R₁ − R₂ = 16 − 25 = −9

Thus, the value of R₁ − R₂ is −9.