Advertisements
Advertisements
प्रश्न
Check whether 7 + 3x is a factor of 3x3 + 7x.
Advertisements
उत्तर १
7 + 3x will be a factor of 3x3 + 7x only if 7 + 3x divides 3x3 + 7x leaving no remainder.
Let p(x) = 3x3 + 7x
7 + 3x = 0
⇒ 3x = −7
⇒ x = `-7/3`
∴ Required remainder
`f(7/3) = 3(-7/3)^3 + 7(-7/3)`
= `3(-343/27) - 49/3`
= `-343/9-49/3`
= `-490/9`
Since `p(-7/3)` ≠ 0
∴ 7 + 3x is not a factor of 3x3 + 7x.
उत्तर २
Let us divide (3x3 + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3x will be a factor of 3x3 + 7x.
By long division,
As the remainder is not zero, therefore, 7 + 3x is not a factor of 3x3 + 7x.
APPEARS IN
संबंधित प्रश्न
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
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)
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Find the values of p and q in the polynomial f(x)= x3 - px2 + 14x -q, if it is exactly divisible by (x-1) and (x-2).
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
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) = 3x3 + 7x2 – 5x + 1
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’.
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 2x2 – 4x – 1, g(x) = x + 1
If x25 + x24 is divided by (x + 1), the result is ______.
