Advertisements
Advertisements
प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
उत्तर
By remainder theorem we know that when a polynomial f(x) is divided by x – a, then the remainder is f(a).
Let f(x) = 2x3 + 3x2 – 5x – 6
f(–2) = 2(–2)3 + 3(–2)2 – 5(–2) – 6
= –16 + 12 + 10 – 6
= 0
Thus, (x + 2) is a factor of the polynomial f(x).
APPEARS IN
संबंधित प्रश्न
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Using the Remainder Theorem find the remainders obtained when ` x^3 + (kx + 8 ) x + k ` is divided by x + 1 and x - 2 .
Hence find k if the sum of the two remainders is 1.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(x2 − 7x + 9) ; (x + 1)
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).
The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.
