Advertisements
Advertisements
प्रश्न
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Advertisements
उत्तर
Let p(y) = y3 − 5y2 + 7y + m
When the polynomial is divided by (y + 2), the remainder is 50. This means that the value of the polynomial when y = −2 is 50.
By remainder theorem,
Remainder = p(−2) = 50
∴ (−2)3 − 5 × (−2)2 + 7 (−2) + m = 50
⇒ − 8 − 5 × 4 -14 + m = 50
⇒ − 8 − 20 − 14 + m = 50
⇒ − 42 + m = 50
⇒ m = 50 + 42 = 92
Thus, the value of m is 92.
APPEARS IN
संबंधित प्रश्न
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
Use remainder theorem and find the remainder when the polynomial g(x) = x3 + x2 – 2x + 1 is divided by x – 3.
When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 2x2 – 5x + 1
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a.
