Advertisements
Advertisements
Question
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
Advertisements
Solution
(x - 1) = 0 ⇒ x = 1
When we substitute this value in the polynomial, whatever we get as a remainder (say a) should be added so that polynomial is exactly subtracted by the factor.
f(1) = 2 × 1 × 1 × 1 - 3 × 1 × 1 + 7 × 1 - 8 + a = 0
⇒ a = 2
Hence answer = 2
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x+1.
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
Given f(x) = ax2 + bx + 2 and g(x) = bx2 + ax + 1. If x – 2 is a factor of f(x) but leaves the remainder – 15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression. f(x) + g(x) + 4x2 + 7x.
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
A polynomial in ‘x’ is divided by (x – a) and for (x – a) to be a factor of this polynomial, the remainder should be ______.
