Advertisements
Advertisements
प्रश्न
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
Advertisements
उत्तर
Let the required number be k.
Let f(x) = x2 + x + 3 + k
It is given that f(x) is divisible by (x + 3).
∴ Remainder = 0
f(–3) = 0
(–3)2 + (–3) + 3 + k = 0
9 – 3 + 3 + k = 0
9 + k = 0
k = –9
Thus, the required number is –9.
APPEARS IN
संबंधित प्रश्न
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(x2 − 7x + 9) ; (x + 1)
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
When x3 – 3x2 + 5x – 7 is divided by x – 2,then the remainder is
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 6x2 + 2x – 4, g(x) = `1 - 3/2 x`
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.
