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
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
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’.
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
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`
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
