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?
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?
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.
-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.
